The proof by contrapositive of the theorem is "For every real number x, if x is rational, then -3x - 8 is rational."
Assume x is rational, meaning x can be expressed as a ratio of two integers a and b, where b is not equal to zero. Thus, x = a/b.
We want to prove that -3x - 8 is rational. Substituting x = a/b, we get -3(a/b) - 8 = (-3a - 8b)/b.
Since a and b are integers, -3a and 8b are also integers. Thus, the numerator (-3a - 8b) is an integer.
We know that a/b is rational, so b is not equal to zero. Therefore, (-3a - 8b)/b is a ratio of two integers and is therefore rational.
Thus, we have shown that if x is rational, then -3x - 8 is rational, which is the contrapositive of the original theorem.
Therefore, the original theorem is true since its contrapositive is true.
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Assuming that the equations define x and y implicitly as differentiable functions s-y-gt, find the slope of the curve x-by-go at the given value of t xt 1)-41f-9, 2ydytt-0
The slope of the curve x-by-go at the given value of t x = 1,
y´ = 1 is -4.
Given: Slope of the curve x-by-go at the given value of t xt
1)-41f-9, 2ydytt-0
Let x=s-y-gt ---------(1)
Let 2ydytt-0 --------(2)
Differentiating both sides of equation (1) w.r.t 't' ,
we getx´= y´- g...................(3)
Differentiating both sides of equation (2) w.r.t 't' ,
we get y´ = 0..........................(4)
Substitute the value of y´ from equation (4) into (3),
we get x´= -g For the given value of t x = 1 we have to find the slope of the curve x-by-go at this value.
Put the value of x = 1 in equation (1)
y = s-g(1)Using equation (1), differentiate both sides w.r.t 't'
we get x´= y´- g Substitute the value of x´= -g, y´=0, g=4, s= 1 into above equation
we get-4=0-4y´y´ = 1
Therefore, slope of the curve x-by-go at the given value of t x = 1, y´ = 1 is -4i.e. slope = -4.
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1) A live action role-playing game (LARP) is a form of role-playing game where the participants physically portray their characters in a fictional setting, while interacting with each other in character. There are game rules to dictate the interactions between players and to determine the winner of the games. A local gamemaster would like to determine how many people in the area would be interested in participating in his LARPing event. He sent out a survey to 1500 people in the area and asked if they would be interested in participating. 432 people said that they would be interested in participating in a LARPing event. (a) State the parameter our confidence interval will estimate. (b) Identify each of the conditions that must be met to use this procedure, and explain how you know that each one has been satisfied. (c) Find the appropriate critical value and the standard error of the sample proportion. (d) Give the 95% confidence interval. (e) Interpret the confidence interval constructed in part (d) in the context of the problem.
Based on the given information, it is explicitly mentioned whether the sample was randomly selected. This means that, based on the sample data, we can estimate the range within which the true proportion of interested participants is likely to fall with 95% confidence.
What is sample?In statistics, a sample refers to a subset of a population that is selected for analysis or study in order to make inferences about the entire population. It is often not feasible or practical to collect data from an entire population, so a sample is used as a representative subset to gather information and draw conclusions about the larger population.
Here,
(a) The parameter that the confidence interval will estimate is the proportion of people in the area who are interested in participating in the LARPing event.
(b) The conditions that must be met to use a confidence interval procedure for a proportion are:
Random Sample: The survey respondents must be randomly sampled from the population of interest. This ensures that the sample is representative of the population.
Large Sample Size: The sample size must be sufficiently large, typically with at least 10 successes and 10 failures in the sample. This ensures that the sampling distribution of the sample proportion is approximately normal.
Independence: The responses of the survey respondents must be independent of each other. This means that one respondent's answer should not influence the answer of another respondent.
Based on the given information, it is not explicitly mentioned whether the sample was randomly selected or whether the sample size is large enough, and whether the responses are independent. This information would need to be provided or assumed in order to determine if the conditions for using a confidence interval procedure for a proportion have been met.
(c) The appropriate critical value can be found using a table or calculator. For a 95% confidence interval, the critical value is 1.96. The standard error of the sample proportion can be found using the formula:
SE = √(p(1-p)/n)
where p is the sample proportion and n is the sample size. Plugging in the values from the problem, we get:
SE = √(0.288(1-0.288)/1500)
= 0.020
(d) The 95% confidence interval can be calculated using the formula:
sample proportion ± (critical value) x (standard error)
Plugging in the values from the problem, we get:
0.288 ± 1.96 x 0.020
= 0.288 ± 0.0392
The 95% confidence interval is (0.2488, 0.3272).
(e) The interpretation of the confidence interval constructed in part (d) would be: We are 95% confident that the true proportion of people in the area who are interested in participating in the LARPing event lies between the lower and upper bounds of the confidence interval. The larger the confidence interval, the less precise our estimate, but the higher our level of confidence in the range.
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What is the equation to 5 less than the product of a number squared and 8
Answer:
8n² - 5Step-by-step explanation:
5 less than the product of a number squared and 8, translating the expression:
n²*8 - 5=8n² - 5Freshman and sophomores were surveyed during lunch about their favorite professional football team.
A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent. The second bar is labeled Dolphins, with freshman from 0 to 45 percent and sophomores from 45 to 100 percent, and the third bar is labeled Buccaneers, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent.
If 140 students selected Jaguars, how many of those students are freshman?
56 students
63 students
77 students
84 students
Answer:
56 students
Step-by-step explanation:
If 40% of students who picked Jaguars are freshmen, and the total who picked it is 140 means \(140\times0.4 = 56\)
Hope this helps!!!
Calculate the 95% confidence interval for the following fictional data regarding daily TV viewing habits: µ= 4.7 hours; σ= 1.3 hours; sample of 78 people, with a mean of 4.1 hours.
We can be 95% confident that the true population mean TV viewing time is between 3.812 and 4.388 hours.
To calculate the 95% confidence interval, we use the formula:
CI = x' ± Zα/2 * (σ/√n)
Where:
x' = sample mean
Zα/2 = the Z-score associated with the desired confidence level (in this case, 95%, so Zα/2 = 1.96)
σ = population standard deviation
n = sample size
Substituting the given values, we get:
CI = 4.1 ± 1.96 * (1.3/√78)
Calculating the standard error (SE) first:
SE = σ/√n
SE = 1.3/√78
SE ≈ 0.147
Then we substitute the SE value in the CI formula:
CI = 4.1 ± 1.96 * 0.147
CI = 4.1 ± 0.288
CI = (3.812, 4.388)
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62X + 310 =
2542 Find X
Answer:
36
Step-by-step explanation:
62x + 310 = 2542
62x = 2232
x = 36
Answer:
36
Step-by-step explanation:
62x + 310 = 2542
Subtract 310 from both sides
62x = 2,232
Then Divide by 62
x = 36
Enjoy.
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 67. Let μ denote the true average compressive strength.
(a) What are the appropriate null and alternative hypotheses?
(b) Let X denote the sample average compressive strength for n = 12 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). If X = 1340, find the P-value. (Round your answer to four decimal places.) P-value = 0.0193
(a) The appropriate null and alternative hypotheses for this scenario are:
Null Hypothesis (H₀): The true average compressive strength is equal to or less than 1300 KN/m².
Alternative Hypothesis (Hₐ): The true average compressive strength is greater than 1300 KN/m²
(b) The p-value for the test statistic X = 1340 is approximately 0.0193
Hypothesis testing:
Hypothesis testing is a statistical method used to make inferences or decisions about a population based on sample data.
To test these hypotheses, a sample of 12 specimens is taken, and the sample mean compressive strength (X) is calculated. The test statistic used in this case is the sample mean itself.
The p-value is then calculated to determine the probability of observing a sample mean as extreme as the observed value (1340) under the assumption that the null hypothesis is true.
(a) The appropriate null and alternative hypotheses for this scenario are:
Null Hypothesis (H₀): The true average compressive strength is equal to or less than 1300 KN/m².
Alternative Hypothesis (Hₐ): The true average compressive strength is greater than 1300 KN/m²
(b) To find the p-value for the given test statistic X = 1340, we need to calculate the probability of obtaining a sample mean as extreme as X, assuming the null hypothesis is true.
Since the sample size is 12 and the population standard deviation is known (σ = 67), use the normal distribution to approximate the sampling distribution of the sample mean.
The test statistic is X itself, and find the probability of obtaining a sample mean as extreme as 1340 or more, given that the null hypothesis is true.
Using the known population standard deviation, calculate the standard error of the sample mean (SE) as σ/sqrt(n), where σ = 67 and n = 12.
=> SE = 67/√(12) ≈ 19.334
To calculate the z-score, subtract the assumed population mean (1300) from the observed sample mean (1340) and divide it by the standard error:
z = (1340 - 1300) / 19.334 ≈ 2.069
Now, find the p-value associated with this z-score using a standard normal distribution table or calculator.
The p-value represents the probability of obtaining a z-score as extreme as 2.069 or more.
Consulting a standard normal distribution table or using a calculator,
Find that the area to the right of 2.069 is approximately 0.0193.
Therefore,
(a) The appropriate null and alternative hypotheses for this scenario are:
Null Hypothesis (H₀): The true average compressive strength is equal to or less than 1300 KN/m².
Alternative Hypothesis (Hₐ): The true average compressive strength is greater than 1300 KN/m²
(b) The p-value for the test statistic X = 1340 is approximately 0.0193.
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The results of a paired-difference test are shown below to the right. d = 5.6
a. Construct and interpret a 99% confidence interval estimate for the paired difference Sd =0.25 in mean values.
b. Construct and interpret a 90% confidence interval estimate for the paired difference n=16 in mean values_ (Round to two decimal places as needed:) Choose the correct answer below:
OA This interval will contain the true population mean 90% of the time_
OB. There is a 90% chance that the true population mean is contained in the interval.
Oc: If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean: 0
D. Approximately 90% of the differences will be contained in the interval.
If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.
When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.
This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.
The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.
In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.
It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.
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Can somebody give me an answer to this it would be really helpful thanks!
Answer:
.625 for decimal, and 62.5 percent.
Step-by-step explanation:
1/8 is 1.25 and that times 5 is .625. .625 * 100 = 62.5
Please give me brainliest
Answer:
The decimal is 0.625
The percent is 62.5%
Step-by-step explanation:
based on the values in the table, what is the smallest number of instances at which the acceleration of the plane could equal zero on the open interval 0 < c < 6?
The smallest number of instances at which the acceleration of the plane could equal zero on the open interval 0 < c < 6 is t= 25 to t= 30.
By the mean value theorem, somewhere between t = 0 and t = 15 , v'(t) = 0, because v(15)-v(0)/15-0 = 0. Also somewhere between t=25 and t=30, v'(t) = 0, because v(30) - v(25) / 30 - 25 = 0. This means a(t) = 0 for at least two values of t.
f(t) = 6+cos(t/10)+3sin(7t/40)
a(t) = f'(t) = 1/10 sin (t/10) + 21/40 cos (7t/40)
f'(23) = -.408 miles/min²
Average Velocity = 5.916 miles per minute
Average Speed is characterized as the adjustment of position or displacement of the object (∆x) partitioned when the time interval (∆t) in which the displacement happens. The average speed can be a positive or negative sign on the indication of the displacement of the object.
The total distance that the plane flies in 40 min is 229 miles.
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What are the tax consequences to Euclid from the following independent events? In your computations, do not round intermediate division. If required, round the per share answer to two decimal places. Round all other answers to the nearest dollar. a. Euclid bought 500 shares of common stock five years ago for $50,000. This year, Euclid receives 20 shares of common stock as a nontaxable stock dividend. As a result of the stock dividend, Euclid's per share basis is $ X. b. Assume instead that Euclid received a nontaxable preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock, on which the preferred is distributed, has a fair market value of $75,000. After the receipt of the stock dividend, the basis of the preferred stock is $ X, and the basis of the common stock is Φ
Euclid receives 20 shares of common stock as a nontaxable stock dividend.The basis of the common stock remains the same as in scenario a, which is $96.15 per share.
To calculate the per share basis, we divide the original purchase cost by the total number of shares (including the dividend shares). In scenario b, Euclid receives a nontaxable preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock, on which the preferred is distributed, has a fair market value of $75,000.
The tax consequences involve determining the new basis of the preferred stock and the common stock after the dividend. a. To find the per share basis of Euclid's common stock after receiving the stock dividend, we divide the original purchase cost by the total number of shares. The original purchase cost was $50,000 for 500 shares, which means the per share basis was $50,000/500 = $100. After receiving 20 additional shares as a dividend, the total number of shares becomes 500 + 20 = 520.
Therefore, the new per share basis is $50,000/520 = $96.15. b. In this scenario, Euclid receives a preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock has a fair market value of $75,000. To determine the new basis of the preferred stock, we consider its fair market value.
Since the preferred stock dividend is nontaxable, its basis is equal to the fair market value, which is $5,000.
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The purpose of this document is to provide proof of identity and employment eligibility for the person being hired.
I-9 form
W-4
application
resume
You randomly select one card from a 52-card deck. find the probability of selecting a red six or a black king.
The probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.
To find the probability of selecting a red six or a black king from a 52-card deck, we need to determine the number of favorable outcomes (red six or black king) and divide it by the total number of possible outcomes (52 cards).
There are 2 red sixes (hearts and diamonds) and 2 black kings (spades and clubs) in a deck.
Since we want to select either a red six or a black king, we can add these numbers together to get a total of 4 favorable outcomes.
Since there are 52 cards in a deck, the total number of possible outcomes is 52.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 4 / 52 Probability = 1 / 13
Therefore, the probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.
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How do you find the derivative of the function using the definition of derivative f(x)=10?
The derivative of of f(x) = 10 is 0
The derivative of a function is the measure of the rate of change of the function. They are fundamental to the solution of problems in calculus and differential equations.
Here the function is not changing as 10 is a constant. So, if f(x) = c where c is a constant then f'(x) = 0 as the derivative of a constant is always zero.
Mathematically:
d(f(x))/dx = \(\lim_{h \to 0}\) (f(x+h) - f(x))/h
There is no x to substitute for x + h so no difference is noticed:
\(\lim_{h \to 0}\) (f(x+h) - f(x))/h = \(\lim_{h \to 0}\) (10 - 10)/h = 0
Hence, the derivative of f(x) = 10 is 0
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In a double-slit experiment, bright interference fringes are spaced 1.8mm apart on the viewing screen when the incident light has a wavelength of 630 nm. What will the fringe spacing be if the light is changed to a wavelength of 420 nm
If the incident light changes from a wavelength of 630 nm to 420 nm, the fringe spacing will decrease, resulting in fringes that are closer together.
In a double-slit experiment, when light passes through two narrow slits and hits a viewing screen, interference patterns are observed. The fringe spacing, also known as the separation between adjacent bright fringes, is determined by the wavelength of the incident light. The formula for calculating fringe spacing is given by:
Fringe Spacing = (wavelength * distance from slits to screen) / distance between the slits
Given that the fringe spacing is initially 1.8 mm when the incident light has a wavelength of 630 nm, we can use the formula to calculate the new fringe spacing when the light wavelength changes to 420 nm. Since the distance from the slits to the screen and the distance between the slits remain constant, the only variable that changes is the wavelength. As the wavelength decreases, the fringe spacing will also decrease. Therefore, the fringe spacing will be smaller when the light wavelength is 420 nm compared to when it is 630 nm.
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In figure, the side QR of ∆PQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR= ½ QPR
Step-by-step explanation:
Mark her brainliest dude!!!!
For a fundraiser, a group plans to sell granola bars and bottles of water at the same prices as described in Part A. The group wants the income from the fundraiser to be at least $150.
Choose the inequality to show the number of granola bars x and the number of bottles of water y that must be sold.
A. 1.4x + 0.75 y > 150
B. 1.4x + 0.75y ≥ 150
C. 1.4x + 0.75 < 150
D. 1.4x + 0.75 ≤ 150
Answer:
A
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
they need at least 150 so it has to be greater than or equal to, because all the number that are greater than 150 meet the requirement of being at least 150 and if it is exactly 150 it's still also meets the requirement.
The side length of the square shown is tripled.
3 cm
Which percent of increase is greater the percent of increase for the perimeter of the square or the percent of increase for the area? How
much greater?
The percent of increase for the
is greater
It is
% greater
Answer:
The percentage increase for the area is greater
It is 600% greater
Step-by-step explanation:
Here, we have a square of side length 3 cm
The area of the square is L^2 = 3^2 = 9 cm^2
Perimeter of the square = 4L = 4 * 3 = 12 cm
When we triple the length of the square, its new length becomes 3 * 3 = 9 cm
Area here will be 9 * 9 = 81 cm^2
Perimeter = 4 L = 4 * 9 = 36cm
To calculate percentage change, we use the formula;
(new value - old value)/old value * 100%
For the perimeter;
(36-12)/12 * 100% = 24/12 * 100% = 2 * 100% = 200%
For the area;
(81-9)/9 * 100% = 72/9 * 100% = 8 * 100% = 800%
The percentage increase of the area is greater
How much greater? 800% - 200% = 600%
Draw a model of √12 using perfect squares.
Answer:
2√3
Step-by-step explanation:
√12 =
√4 * √3 =
√2^2 * √3 =
2 * √3 =
2√3
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Answer:
We can write 12 as 4 + 4 + 4, or 4 ∙ 3. So, create three squares that each have two columns and two rows.
a series of 3 squares, each composed of 4 smaller squares
so √12 =√4 x 3 = √4 x √3 = 2√3
Step-by-step explanation:
Find polar coordinates of the point that has rectangular coordinates (3,2). Write your answer using degrees, and round your coordinates to the nearest hundredth.
The polar coordinates of the point that has rectangular coordinates (3, 2) are approximately (3.61, 33.69°).
To find the polar coordinates of a point given its rectangular coordinates, we can use the following formulas:
r = sqrt(x^2 + y^2)
θ = atan2(y, x)
Let's calculate the polar coordinates for the point (3, 2):
r = sqrt(3^2 + 2^2) = sqrt(9 + 4) = sqrt(13) ≈ 3.61
To calculate θ, we'll use the atan2 function, which takes into account the signs of both x and y:
θ = atan2(2, 3) ≈ 33.69 degrees
Therefore, the polar coordinates of the point (3, 2) are approximately (3.61, 33.69°).
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On the coordinate plane, point A is located at ( – 9, – 4) and point B is located at ( – 1,y). The distance between points A and B is 10 units. What are the two possible locations of point B? ,
The two possible locations of point B are (–1, 2) and (–1, –10).
To find the two possible locations of point B, we can use the distance formula:
distance =
\(√[(x₂ - x₁)² + (y₂ - y₁)²]\)
where x₁ and y₁ are the coordinates of point A, and x₂ and y₂ are the coordinates of point B.
We know that the distance between points A and B is 10 units, so we can plug in the values and simplify the equation:
\(10 = √[(-1 - (-9))² + (y - (-4))²]\)
\(10 = √[64 + (y + 4)²]\)
\(100 = 64 + (y + 4)²\)
\(36 = (y + 4)²\)
±6 = y + 4. Solving for y, we get two possible values: y = 2 or y = -10.
These points are located on a vertical line passing through x = –1, with point A being 10 units away in the left direction.
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whats the ratio of 32:40
Answer:
4:5
Step-by-step explanation:
32:40
=>32/40
=>diving numerator and denominator by 8
=>4/5
=>4:5
Answer: 4:5
Step-by-step explanation:
32 and 40 share a common factor of 8. We can divide both of them by 8 so that the ratio stays the same value and it'll be in it's simplest form.
\(\frac{32}{8} =4\\\frac{40}{8} =5\)
4:5 is the final answer.
The lines shown below are perpendicular. If the green line has a slope ofwhat is the slope of the red line?ih510A.1B. 7Oc. -7D.-INان ال۔
Recall that the product of the slopes of two perpendicular lines is equal to
\(-1,\)therefore, if the slope of the green line is 1/7, and x the slope of the blue line we can set the following equation:
\(\frac{1}{7}x=-1.\)Solving for x we get that:
\(x=-7.\)Answer: Option C.
(-4^0) + 1 equals to ?
Answer:
zero (0)
Step-by-step explanation:
-4^0=-1
-1+1=0
Solve for x, round to the nearest tenth
Help please???
Answer:
1.23
Step-by-step explanation: since i helped can i have brainlist please :D
a number is a restriction on a rational expression if the number makes the denominator of the rational expression
A number is a restriction on a rational expression if the number makes the denominator of the rational expression equal to zero.
Hence, option (b) is correct choice.
Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.
A rational expression's denominator is undefined when it equals zero, hence it cannot be employed in the expression.
For that particular value of the number, the limitation renders the value of the rational statement undefinable.
To put it another way, the number is a limitation since it cannot be used as the input for the rational expression because the output would be an undefined value.
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The missing option may be:
(a) 1
(b) 0
(c) always positive
(d) Indefinite
solve pls brainliest
Answer:
y = -6 x I think
Step-by-step explanation:
please give brainliest I tryed
don't guess!! pls help!!
THERE'S 4 IMAGES.
Answer:
pic one is rock cycle, pic 2 crystaline structure, and pic three and 4 are the same pictures as question 2
Step-by-step explanation:
In how many ways can 4 people be chosen and arranged in a straight line if there are 13 people from whom to choose?
Answer:
17160
Step-by-step explanation:
Total number = n = 13
Number required = r= 4
If the number required does not have a specific order then combinations is chosen.
If a specific arrangement is required then permutations is used.
Here a specific arrangement is mentioned therefore
13P4= 17160
A standard yield sign is an equilateral triangle with sides measuring 36
inches. The height of the triangle is approximately 40.5 inches. What is
the area of a standard yield sign?
Answer:
729 sq in
Step-by-step explanation:
Area = 1/2bh
1/2 * 36 * 40.5 = 729 sq in