The radius of the circle will be 4.6m.
What is area of a circle?
The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value. The area of the circle will be A = [tex]\pi r^{2}[/tex].
The area of the circle given is = 15 m²
Sector of a circle with a central angle of 5π/11 rad
The area will be (1/2) * r² * Ф
15 = (1/2) * r² * (5π/11)
⇒r² = 30 * (11/5π)
⇒r² = 21.00
⇒r=4.6m
Hence, the radius of the circle will be 4.6m.
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An experiment consists of 8 independent trials where the probability of success on each trial is 3 8. Find the probability of obtaining the following. Round answers to the nearest ten-thousandth. 13. Exactly 3 successes. 14. Exactly 6 successes.
As each trial has a 0.375 probability, the probability for three successes is 0.05273 and for six successes is 0.00278.
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the probability of a given event by the probability that it won't. By dividing the number of preferable outcomes by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained.
Here,
The probability of success in each trial=3/8
For 3 success,
P(3)=(3/8)³
=0.05273
For 6 success,
P(6)=(3/8)⁶
=0.00278
The probability for 3 success is 0.05273 and for 6 success is 0.00278 as for each trial, the probability is 0.375.
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Jenae noticed that many of her co-workers would opt for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly.Select one control in Jenae's experimental study
Jane makes sure that the (B) coffee is brewed simultaneously in each pot as part of her experimental study.
What is the experimental study?Experimental investigations involve introducing an intervention and observing its results.
Typically, volunteers in experimental research are grouped randomly, or by chance.
In experimental research, the dependent and independent variables are compared to examine how they relate to one another.
A link between a certain feature of an item and the variable under investigation is either accepted or denied following the conclusion of an experimental research study.
Laboratory experiments are the most fundamental type of experimental study, albeit they can take on several forms depending on the research topic.
Laboratory experiments are the most fundamental type of experimental study, albeit they can take on several forms depending on the research topic.
So, in the given situation, Jeane makes sure that the coffee is brewed simultaneously in all of the pots.
Therefore, Jane makes sure that (B) coffee is brewed simultaneously in each pot as part of her experimental study.
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Complete question;
Jenae noticed that many of her co-workers would opt for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly. Select one control in Jenae's experimental study:
a. Jeane places condiments at random places throughout the kitchen.
b. Jeane makes sure that the coffee in different pots is brewed at the same time.
c. Jeane uses different locations in the kitchen for the coffee pots.
d. Jeane monitors the habit of co-workers who do not drink coffee.
Determine if the expression for r(u, v) with domain D defines a smooth parametrized surface. Explain your answer. (Your instructors prefer angle bracket notation < > for vectors.) r(u, v) = (cos(u), sin(v), 1), D = {(u, v) | 0 Sus 41,0 S V S 41} r(u, v) with domain D ---Select--- v define a smooth parametrized surface. To be a smooth parametrized surface (", xru(u, v) # O for all (u, v) in the interior of the domain. In this case (?, *Tv , therefore there ---Select--- v (u, v) where (FoxPv)(u, v) = 7.
The Vector r(u, v) with the domain D does not define a smooth parametrized surface.
Vector: Vectors are quantities that can be identified by magnitude and direction. Examples are velocity and acceleration.
Given that:
Vector r(u, v) = (cos(u), sin(v), 1), D = {(u, v)
Vector [tex]r_{u}[/tex] = (-sinU, 0,0)
Vector [tex]r_{V}[/tex] = (0, cosv,0)
Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] =
[tex]\left[\begin{array}{ccc}i&j&k\\-sinU&0&0\\0&cosv&0\end{array}\right][/tex]
Solving the vector multiplication. We get,
Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = 0 x i - j x 0 + (cosv x - sinU)
Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = 0 - sinUcosv
Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = - sinUcosv
Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = (0, 0,- sinUcosv)
The Vector r(u, v) with the domain D does not define a smooth parametrized surface.
Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = (0, 0,- sinUcosv) therefore has some value.
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Solve the following inequality for pp. Write your anwer in implet form. -5p -1 > -10p - 2
The value of the variable 'p' for the given inequality is found as p > -1/5.
Explain the term inequality?In mathematics, "inequality" refers to a relationship involving two variables or values that is not equal to one another and. Therefore, inequality emerges from a lack of balance.For the stated question-
-5p -1 > -10p - 2
Solve the inequality as
Add 1 both sides.
-5p -1 + 1 > -10p - 2 + 1
-5p > -10p - 1
Add 10p both sides.
-5p + 10p > -10p - 1 + 10p
5p > -1
Divide both sides by 5
p > -1/5
Thus, the value of the variable 'p' for the given inequality is found as p > -1/5.
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Which inequality is shown in the graph?
A. y−5 < −5/3(x+6)
B. y−5 > −5/3(x+6)
C. y+5 < −5/3(x−6)
D. y+5 > −5/3(x−6)
Is the function even, odd, or neither?
The correct option is the third one, the function is neither odd nor even.
Is the function even, odd, or neither?
A function y = f(x) is an odd function if for all values of x in its domain:
f(x) = f(-x)
The graph of these functions have an axis of symmetry at the y-axis.
And it is an odd function is for all values of x in its domain:
f(x) = -f(x)
These functions "invert" at the y-axis,
Now let's look at the graph.
When x = 5, we can see that:
f(x) = 9
And when x = -5, the function is:
f(-5) = -0.5
Neither of the conditions is meet.
Then the function is neither odd nor even.
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when two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would evidently provide the better fit is the one with a .
The regression model that would offer the better fit is one with a smaller standard error of the estimation and a given elements coefficient of determination when two regression models used on the same data set have had the same dependent variables but a variable figure of explanatory factors.
The coefficient of determination is most frequently used to determine how well a regression model fits observed data. For instance, data fitting the regression model 60% of the time is indicated by a determination coefficient of 60%. In general, a greater coefficient denotes a better model fit.
The degree of deviation around the mean increases with the coefficient of variation. Typically, a percentage is used to indicate it. Without units, it enables comparison of value distributions whose measurement scales are incomparable.
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what is the equation in point-slope form of a line that passes through the points (7, −8) and (−4, 6) ? responses y+6=−23(x−4) y plus 6 equals negative fraction 2 over 3 end fraction open parenthesis x minus 4 close parenthesis y+6=−1411(x−4) y plus 6 equals negative fracion 14 over 11 end fraction open parenthesis x minus 4 close parenthesis y−6=−23(x+4) y minus 6 equals negative fraction 2 over 3 end fraction open parenthesis x plus 4 close parenthesis y−6=−1411(x+4)
The equation of the line that passes through the points (7, -8) and (-4, 6) in point slope form is y - 6 = -14/11(x + 4)
The coordinates of the first point = (7, -8)
The coordinates of the second point = (-4, 6)
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (6-(8) / (-4-7)
= 6+8 / -4-7
= 14 / -11
= - 14/11
Point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the value in the equation
y - 6 = -14/11(x - (-4))
y - 6 = -14/11(x + 4)
Therefore, the equation of the line is y - 6 = -14/11(x + 4)
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The function f(x)=lnx has a Taylor series at a=6. Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms.
The Taylor series expansion of f of x is given by 11e to the fourth power + 22e to the fourth power times x minus two plus 22e to the fourth power multiplied by x minus two all squared, where f of x is equal to 11e to the power of two x in rising powers of x minus two.
What is Taylor series?An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.
Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions.
For Brook Taylor, who introduced the Taylor series in 1715, they are named after him. When 0 is the point at which the derivatives are taken into account, a Taylor series is also known as a Maclaurin series in honor of Colin Maclaurin, who made great use of this unique situation of Taylor series in the middle of the 18th century.
The nth Taylor polynomial of a Taylor series is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series.
Hence, The Taylor series expansion of f of x is given by 11e to the fourth power + 22e to the fourth power times x minus two plus 22e to the fourth power multiplied by x minus two all squared, where f of x is equal to 11e to the power of two x in rising powers of x minus two.
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Two students, Jessica and Steve, are solving the math problem below: A hiker is hiking at an elevation located 18 meters above sea level. Simultaneously a diver is diving at a location that is 12 meters below sea level. Find the distance between the two elevations. The students came up with different answers. Jessica said the answer is 6 meters. Steve said the answer is 30 meters. Who is correct?
The distance between the two elevation is 30 metres. Therefore, Steve is correct.
How to find the distance between the two elevations?A hiker is hiking at an elevation located 18 meters above sea level. Simultaneously a diver is diving at a location that is 12 meters below sea level.
The distance between the two elevation can be calculated as follows:
Jessica said the answer is 6 meters. Steve said the answer is 30 meters.
Let's find who is correct.
The hiker is 18 metres above sea level . The diver is 12 meters below sea level. For the diver to get to sea level he will travel 12 meters. For the diver to get to the hiker position he will travel extra 18 metres.
Therefore, the distance in elevation is 12 + 18 = 30 metres. Hence, Steve is correct.
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tom went on a bike ride. after 6 miles he got a flat tire and had to jog back home. he jogs 3 mph slower than he bikes, so the jog took 1 hour longer than the bike ride. at what rate did he travel each way?
Tom Pedalled his bike at a pace of 6 km/h and ran at a speed of 3 km/h.
Given,
Tom went on a bike ride;
Distance covered = 6 miles
Speed of bike = x
Speed of jogging = x - 3
Jogging is one hour more than bike ride
That is,
(6/x - 3) - (6/x) = 1
6 (x - x + 3 / x(x - 3)) = 1
18 / x² - 3x = 1
x² - 3x = 18
x² - 3x - 18 = 0
x² - 6x + 3x - 18 = 0
x(x - 6) + 3(x - 6) = 0
(x + 3) (x - 6) = 0
x = 6
That is,
Tom travelled at a speed of 6 km/hr with bike and 3 km/hr by jogging.
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0.5 power of 2 - 0.3 power of 2
Answer: 0.16
Step-by-step explanation:
Enter the data below into a calculator to find the correlation coefficient, the regression line equation, and the strength of the linear correlation:
x y
1 6
2 1
3 5
4 2
5 4
6 3
7 7
8 8
9 6
Correlation Coefficient (enter a decimal rounded to the nearest hundredth):
Equation of the regression line (enter as an equation in the form y=mx+b, no spaces, decimals rounded to the nearest hundredth):
Strength of the linear correlation (type one of the following exactly: "Perfect Negative", "Strong Negative", "Moderate Negative", "Weak to No", "Moderate Positive", "Strong Positive", or "Perfect Positive". Watch for spelling!):
Answer:
I guess it's 77 although I'm not in high school
A company that manufactures memory chips for digital cameras uses the formula c = 3√n(40 6√n +9 4√n) to determine the cost, c, in dollars, for producing n chips. This formula can be written as c = 120 3√n +27 4√nb, where a and b are constants.
What are the values of a and b?
**answer choices in pic
The values of a and b are 3 and 2.
What is Expression?An expression is combination of variables, numbers and operators.
Given,
A company that manufactures memory chips for digital cameras uses the formula [tex]c=3\sqrt{n} (40\sqrt[6]{n}+9\sqrt[4]{n} )[/tex]
The cost, c, in dollars, for producing n chips.
We need to solve for values a and b.
[tex]c=3\sqrt{n} (40\sqrt[6]{n}+9\sqrt[4]{n} )[/tex]
[tex]c=3\sqrt{n} (40\sqrt[6]{n})+3\sqrt{n} (9\sqrt[4]{n} )[/tex]
[tex]c=120\sqrt{n} \sqrt[6]{n} +27\sqrt{n} \sqrt[4]{n}[/tex]
[tex]c=120n^{\frac{7}{2}} +27n^{\frac{5}{2}}[/tex]
c=[tex]120n^{\frac{3a}{2} } +27n^{\frac{4b}{2} }[/tex]
By solving this we get a=3 and b=2
Hence, the value of a and b is 3 and 2.
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In a study to compare the perceived effects of two pain relievers, 200 randomly selected adults were given the first pain reliever, and 93% indicated appreciable pain relief. Of the 450 individuals given the other pain reliever, 96% indicated experiencing appreciable relief. A give an estimate for the difference in the proportions of all adults who would indicate perceived pain relief after taking the two pain relievers. Provide a bound on the error of estimation. B based on your answer to part (a), is there evidence that proportions experiencing relief differ for those who take the two pain relievers? why
7% people would indicate perceived pain relief after taking the two pain relievers.
What is error of estimation?
The difference between an estimated value and the true value of a parameter or, sometimes, of a value to be predicted is an error of estimation.
Evaluation :Given that,In a study comparing the perceived effects of two painkillers, 200 randomly chosen persons were given the first one, and 93% reported noticeably lessening of their pain.
96% of the 450 people who received the other painkiller reported feeling noticeably relieved.We have to estimate the percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.
Give the estimate 95% confidence interval.
We know that
,p=(186+432)/(200+450)p=0.95
We getL.B= 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)
L.B= 0.07
U.B = 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)
U.B = 0.01
Bound of error = 096√0.95(1-0.95)(1/200+1/450) = 0.04
∴ 7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.
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A student is taking a multiple-choice test in which each question has four possible answers. She knows the answers to 5 of the questions, can narrow the choices to 2 in 3 cases, and does not know anything about 2 of the questions. What is the probability that she will correctly answer A) 10, b) 9, c) 8 d) 7, e) 6, and f) 5 questions?
Do not need to answer every part if they are worked the EXACT same way.
the probability that she will correctly answer
A) 10 questions = 0
b) 9 questions = 0.00003
c) 8 questions = 0.00039
d) 7 questions =0.00309
e) 6 questions = 0.01622
f) 5 questions = 0.0584
Here the total number of question is 5+3+2= 10, and every question has four possible answers, for this problem, we will be using the binomial distribution, the formula is :
[tex]C_{n,k}[/tex][tex]p^{k}[/tex][tex]q^{n-k}[/tex] ,here C is the combination, p is the probability of success and q is the probability of having the success
for the given situation :
the p = 1/ 4 whereas, q=3/4
here n =10
now for different values of k which is the number of successes, we substitute the know values in the formula, and we get
P(k=10) = 0
P(k=9) = 0.00003
P(k=8) = 0.00039
(P=7)= 0.00309
(P=6)=0.01622
(P=5)= 0.0584
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CNNBC recently reported that the mean annual cost of auto insurance is 1037 dollars. Assume the standard deviation is 243 dollars. You take a simple random sample of 69 auto insurance policies. (Do not use tables unless directed to do so.)
Find the probability that a single randomly selected value is more than 987 dollars.
P(XÂ > 987) =Â
Find the probability that a sample of size n=69 is randomly selected with a mean that is more than 987 dollars.
P(¯x > 987) =Â
Enter your answers as numbers accurate to 4 decimal places.
The probability that a single randomly selected value is more than 987 dollars is 0.5664
We know that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.
We know very well that z-value is calculate by the formula
z = (X-μ) / σ/√n
where z is the z-value,
X is randomly selected value,
μ is standard mean
σ is standard deviation and
n is the sample size.
For, X=987
=>z = (987-1037) / (243/√69)
=>z= -50 / (243 / 8.33)
=>z = -50 / (29.171)
=>z= -1.714
Now, we need to find the probability of A>987,so,we need to find what is the probability of A<=987.
P(X>987)= 1-P(X≤987)
=>P(X>987)=1-P(z<(-1.714))
Using the z-table ,we get that P(z<(-1.714))=0.43353
Therefore, P(X>987)=1-0.43353=0.5664
Hence, required probability is 0.5664
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(Complete question) is:
CNNBC recently reported that the mean annual cost of auto insurance is 1037 dollars. Assume the standard deviation is 243 dollars. You take a simple random sample of 69 auto insurance policies. (Do not use tables unless directed to do so.)
Find the probability that a single randomly selected value is more than 987 dollars. P(Â > 987).Enter your answers as numbers accurate to 4 decimal places.
The number of sweets
s
that each friend gets is the number of sweets in a box
n
divided by the number of friends
f
the sweets are shared between. Enter a formula for the number of sweets each friend gets and enter the number of sweets each friend gets if there are 48 sweets and 8 friends.
The number of sweets each friend gets = 6
The number of sweets s that each friend gets = the number of sweets in a box n ÷ number of friends f the sweets are shared between
s = n ÷ f
s = n/ f
if there are 48 sweets and 8 friends.
That is,
n = 48 sweets
f = 8 friends
Find s,
s = n/ f
= 48 / 8
= 6
s = 6 sweets
The number of sweets each friend gets = 6
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in a specific university, getting a full scholarship and getting an internship are conditionally independent given that you are a top student. it is known that 50% of top students get a full scholarship and 40% of top students get an internship. if a randomly selected student is known to be a top one, what is the probability they will get a full scholarship and an internship? assume event a: getting a full scholarship; event b: getting an internship; event c: being a top student.
The probability they will get a full scholarship and an internship Is 0.2
What is Probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
However, if two coins are tossed, four outcomes might occur: (H, H), (H, T), (T, H), and (T, T).
For instance, when we flip a coin, there are just two potential results: Head OR Tail (H, T).
Given that these two events are independent. Hence,
P(Full scholarship and an internship)
= P(Full scholarship) * P(Internship)
= 0.50 * 0.40
= 0.20
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Can the following side lengths form a triangle?
5 inches
2 inches
3 inches
A Yes
B No
c Maybe
Answer:
Step-by-step explanation:
the longest sideis greater than others.
so the answer is
Answer:
Yes it can
Step-by-step explanation:
Three sides of any length will always form a triangle.
What is 8.123 as a decimal number
Answer: 8.123 is a decimal
Step-by-step explanation:
A decimal is a whole number and a fractional part
there is a decimal point
a company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122.5 grams per apple. is there sufficient evidence to reject the company’s claim? (useα
We fail to reject H0. So there is enough evidence to state that the hypothesis H1 has the risk to make an error equal to α.
What do you mean by standard deviation?
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A lower number deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
What does it mean if standard deviation is negative?The standard deviation is positive, or greater than zero, whenever there are two uneven terms in the observations. The standard deviation is exactly zero if all of the observations are equally distributed. Thus, the standard deviation can never be negative or less than zero.
We have two hypotheses:
H0: μ= 120
H1: μ≠ 120
where μ is the mean weight and per apple the value of α is 0.05. If conditions are met we will run sample a.
random: 49 apples are randomly selected
normal: 49>=30 so CLF holds. Now,
formula of z-test for μ
Test statistic: z-test=(¯x−μ)/( σ/√n)
We are given with:
n=49
¯x=122.5
σ=12
putting values in formula:
z-test=(122.5-120)/(12/√49)
=1.458
P-value: P(z>1.458)=normal df(1.458, ∞,1)
=0.0724
And it is a two tailed test so
=2(0.0724)
=0.1448
Since P-value> α ; (0.0724>0.05)
So, we fail to reject H0. We do not have convincing evidence that there is a difference in mean weight per apple. So here we would say that there is enough evidence to state that the hypothesis H1 has the risk to make an error equal to α.
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The relationship between hours practice and coordinate video game is modeled by the equation Y = 10x graph this relationship on the graph below what is the slope and what does it mean for the situation
answer:
provided in the explanation.
step-by-step explanation:
the graph would contain the points (0,0), (1,10), (2,20), etc. the slope is 10, which represents the number of coordinate video games practiced in x number of hours. the representation for the slope depends on whether coordinate video game or hours practiced is on the x or y axis. hope that helps!
which of the following is not a requirement for constructing a confidence interval for estimating the population proportion? question content area bottom part 1 choose the correct answer below. a. there are at least 5 successes and 5 failures. b. the trials are d
The option B "The trials are done without replacement" is not a requirement for constructing a confidence interval for estimating the population proportion.
In the given question we have to check which of the following is not a requirement for constructing a confidence interval for estimating the population proportion?
The given options are:
a. There are at least 5 successes and 5 failures.
b. The trials are done without replacement.
c. The sample is a simple random sample.
d. There is fixed number of trials.
As we know that, an estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.
As given that we have to find which of the following is not a requirement for constructing a confidence interval for estimating the population proportion. So for constructing a confidence interval for estimating the population proportion, we can find the trials without replacement.
So the option B "The trials are done without replacement" is correct.
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which sentance describe points that miguel should consider in the goal setting process before he starts to invest
the edges of a rectangular solid have these measures: 1.5 feet by 1½ feet by 3 inches. what is its volume in cubic inches?
The volume of the rectangular solid with the given measures is equal to 972 cubic inches.
As given in the question,
Measures of edges of rectangular solid is given by :
1.5 feet by 1 1/2 feet by 3 inches
Conversion of feet to inches:
1 feet = 12 inches
Let length = 1.5 feet
= 1.5 × 12
= 18inches
Width = 1 1/2 feet
= ( 3/2 ) × 12
= 18 inches
Height = 3 inches
Volume of the rectangular solid
= length ×width ×height
= 18 × 18 × 3
= 972 cubic inches
Therefore, the volume of the rectangular solid is equal to 972cubic inches.
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A manufacturer of refrigerators must ship at least 100 refrigerators to its two warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 25
Krefrigerators already, while warehouse B has 20 on hand. It costs $15 to ship a refrigerator to warehouse A and $10 to ship one to warehouse B. How many refrigerators
should be shipped to each warehouse to minimize cost? What is the minimum cost?
The minimum cost is 12.
what is the largest positive integer n for which there is a unique integer k such that 8 15 < n n k < 7 13 ?
the largest positive integer n[tex]\leq[/tex]112 for which there is a unique integer k
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Given inequality is
[tex]\frac{15}{8} < \frac{n+k}{k} < \frac{13}{7}[/tex]
[tex]\frac{8}{15} < \frac{n}{n+k} < \frac{7}{13}[/tex]
[tex]n\frac{6}{7} < k < n\frac{7}{8}[/tex]
[tex]n\frac{7}{8}-n\frac{6}{7}[/tex] > 2
n[tex]\leq[/tex]112
Hence, the largest positive integer n[tex]\leq[/tex]112 for which there is a unique integer k
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find the equation of the line that is perpendicular to the line 5x-2y=12
The slope of two perpendicular lines is the negative inverse of each other thus the equation of the perpendicular line will be y = (-2/5)x + c.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given line,
5x-2y=12
2y = 5x - 12
y = (5/2)x - 6
The slope of the above line is 5/2
Since the slope of two perpendicular lines is the negative inverse of each other.
Thus,slope of line = -1/(5/2) = -2/5
So equation will be y = (-2/5)x + c
Hence"The slope of two perpendicular lines is the negative inverse of each other thus the equation of the perpendicular line will be y = (-2/5)x + c".
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five-team tournament, each team plays one game with every other team. each team has a 50% chance of winning any game it plays. (there are no ties.) let m n be the probability that the tournament will produce neither an undefeated team nor a winless team, where m and n are relatively prime integers. find m n
The value of integers m and n is 17 and 32 respectively.
Here, we are given that in a five-team tournament, each team plays one game with every other team.
Chance of winning = 50% or 1/2
We need to find the probability that at least one team wins all games or at least one team loses all games. We can use complementary counting to do so.
Each team will play 4 matches.
Probability that there is one team which wins all games = [tex]5*1/2^{4}[/tex]
= 5/16
Similarly, the probability that there is one team which loses all games = 5/16
The probability that one team wins all games and another team loses all games = [tex][5(1/2)^{4} ][4(1/2^{3})][/tex]
= (5/16)(4/8)
= 5/32
Now, 5/16 + 5/16 - 5/32 = 15/32
Since this is the complement of the probability we want, we subtract it from 1 to get (1- 15/32) = 17/32
Thus, the value of integers m and n is 17 and 32 respectively.
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