Answers
Given:
Given that the measurements of the triangle.
We need to determine the value of x.
Value of x:
The value of x can be determined using by angle bisector theorem.
The angle bisector theorem states that "if the angle that bisects the triangle will divide the opposite sides into two segments that are proportional to the remaining two sides of the triangle".
Hence, applying the theorem, we have;
[tex]\frac{x}{20-x}=\frac{14}{11}[/tex]
Cross multiplying, we get;
[tex]11x=14(20-x)[/tex]
Simplifying, we get;
[tex]11x=280-14x[/tex]
[tex]25x=280[/tex]
[tex]x=11.2[/tex]
Thus, the value of x is 11.2
Related Questions
A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the flow rate be more than 5 gallons per minute (gpm). In an initial study, eight runs were made. The average flow rate was 6.5gpm and the standard deviation was 1.9 gpm. If the mean flow rate is found to meet the specification, the pump will be put into service.
1. State the appropriate null and alternate hypotheses
2. Find the P-value
3. Should the pump be put into service? Explain.
Answers
Answer:
1) We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 5[/tex]
Alternative hypothesis:[tex]\mu > 5[/tex]
2) [tex]df=n-1=8-1=7[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(7)}>2.233)=0.0304[/tex]
3) For this case is we use a significance level of 1% or 99% of confidencewe see that [tex]p_v >\alpha[/tex] and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance [tex]\alpha=0.05[/tex] or 95% of confidence we see that [tex]p_v <\alpha[/tex] and we have enough evidence to conclude that the specification is satisfied.
Step-by-step explanation:
Data given and notation
[tex]\bar X=6.5[/tex] represent the sample mean
[tex]s=1.9[/tex] represent the sample standard deviation
[tex]n=8[/tex] sample size
[tex]\mu_o =5[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
Part 1: State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 5[/tex]
Alternative hypothesis:[tex]\mu > 5[/tex]
If we analyze the size for the sample is <30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{6.5-5}{\frac{1.9}{\sqrt{8}}}=2.233[/tex]
Part 2: P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=8-1=7[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(7)}>2.233)=0.0304[/tex]
Part d: Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant higher compared to the height of men in 1960 at 1% of signficance.
Part 3
For this case is we use a significance level of 1% or 99% of confidencewe see that [tex]p_v >\alpha[/tex] and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance [tex]\alpha=0.05[/tex] or 95% of confidence we see that [tex]p_v <\alpha[/tex] and we have enough evidence to conclude that the specification is satisfied.
A brownie recipe calls for 1 cup of sugar and 1/2 cup of flour
Answers
Answer:
Uhhhhhhhhhhhhh yes most recipies do call for that
Step-by-step explanation:
have a nice day
80% of 25 is equal to what
Answers
Answer:
20
Step-by-step explanation:
Of means multiply and is means equals
80% * 25 = ?
Change to decimal form
.80 *25 =
20
Is this expression true or false? 5 ÷ 1/9 = 45
Answers
Answer:
False
Step-by-step explanation:
Common sense
Standardization of a Normal Distribution: Bryce reads in the latest issue of Pigskin Roundup that the average number of rushing yards per game by NCAA Division II starting running backs is 50 with a standard deviation of 8 yards. If the number of yards per game (X) is normally distributed, what is the probability that a randomly selected running back has 64 or fewer rushing yards
Answers
Answer:
[tex]P(X<64)=P(\frac{X-\mu}{\sigma}<\frac{64-\mu}{\sigma})=P(Z<\frac{64-50}{8})=P(z<1.75)[/tex]
And we can find this probability using the normal standard table or excel and we got:
[tex]P(z<1.75)=0.9599[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the number of rushing yards of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(50,8)[/tex]
Where [tex]\mu=50[/tex] and [tex]\sigma=8[/tex]
We are interested on this probability
[tex]P(X<64)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X<64)=P(\frac{X-\mu}{\sigma}<\frac{64-\mu}{\sigma})=P(Z<\frac{64-50}{8})=P(z<1.75)[/tex]
And we can find this probability using the normal standard table or excel and we got:
[tex]P(z<1.75)=0.9599[/tex]
In a recent survey in a Statistics class, it was determined that only 74% of the students attend class on Fridays. From past data it was noted that 88% of those who went to class on Fridays pass the course, while only 20% of those who did not go to class on Fridays passed the course.
a.What percentage of students is expected to pass the course?
b.Given that a person passes the course, what is the probability that he/she attended classes on Fridays?
Answers
Answer:
a) 83%
b) 0.892
Step-by-step explanation:
percentage that attends class on friday = 74%
percentage that pass because they attend class on friday = 88%
percentage that pass but did not go to school on friday = 20%
a) percentage of students expected to pass the course
= (74% x 88%) +(88% x 20%)
= 0.6512 + 0.176
= 0.8272
= 83%
b) If a person passes the course, what is the probability that he/she attended classes on Fridays
= 74% divided by 83%
= 0.892
Find the x-coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, minimum, or neither by first applying the second derivative test, and, if the test fails, by some other method. f(x) = 5x^6 − 10x^4
Answers
Answer:
x = 0, local maximumx = ±(2/3)√3, global minimaStep-by-step explanation:
The first derivative is ...
f'(x) = 30x^5 -40x^3 = 10x^3(3x^2 -4)
This will have zeros (critical points) at x=0 and x=±√(4/3).*
We don't need the second derivative to tell the nature of these critical points. Since the degree is even, the function is symmetrical about x=0. Since the leading coefficient is positive, it generally has a U-shape. This means the "outer" critical points will be minima, and the central one will be a local maximum.
__
However, since we're asked to use the 2nd derivative test first, we find the 2nd derivative to be ...
f''(x) = 150x^4 -120x^2 = 30x^2(5x^2 -4)
For x=0, f''(0) = 0 -- as we expect for a function with a high multiplicity of the root at that point. For x either side of zero, both the function and the second derivative are negative, indicating downward concavity. That is, x = 0 is a local maximum.
For x² = 4/3, the second derivative is positive, indicating upward concavity. At x = ±√(4/3), we have local minima.
_____
* The "simplified" equivalent to √(4/3) is (2/3)√3.
The critical points of the function f(x) = 5x^6 − 10x^4 are x = 0, x = ±√(4/3). The point at x = 0 is a relative maximum while the points at x = ±√(4/3) are relative minima based on the second derivative test.
Explanation:Given the function f(x) = 5x^6 − 10x^4, we first find the critical points. This is done by finding the derivative of the function and setting it equal to zero. For this function, the derivative, f'(x), is 30x^5 - 40x^3 = 0. Solving this equation for x, we get x = 0, and x = ±√(4/3).
Next, we apply the second derivative test by taking the second derivative of the original function, f''(x). This gives us f''(x) = 150x^4 - 120x^2. We substitute the obtained critical points into the second derivative. If f''(x) > 0, then the point is a relative minimum, if f''(x) < 0, it's a relative maximum. If neither, we need to consider higher order derivatives or other methods.
The second derivative is negative at x = 0, so that position is a relative maximum. The second derivative is positive at x = ±√(4/3), so these positions are relative minima.
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Please help me in don't understand how to do this
Answers
Answer:
36
Step-by-step explanation:
[tex] \frac{c}{4} - 5 = 4 \\ \\ \frac{c}{4} = 4 + 5\\ \\ \frac{c}{4} = 9 \\ \\ c = 9 \times 4 \\ \\ \huge \red{ \boxed{ c = 36}}[/tex]
You are at a campus party where there are a total number of n people. The host asked everyone to put their phones in a bowl while walking in. A noise complaint ends the party abruptly, and everyone heads for the door, hastily grabbing their phones from the bowl Assume every guest has one and exactly one phone, and that they pick a phone at random (so that every assignment of a phone to a person is equally likely). What is the probability that: a. Every person gets their phone back? b. The first m persons to pick each get their own phones back? c. The first m persons to pick each get a phone belonging to the last m persons to pick? Hint: Try this thought experiment with a few choices of mand n to get a feel for the numbers that show up.)
Answers
Answer:
1, [tex]\frac{m}{n}[/tex], [tex]\frac{1-m}{n}[/tex].
Step-by-step explanation:
probability = [tex]\frac{Number of Possible Outcomes}{Total Outcomes}[/tex]
Total number of persons in the party = n
a) Pr ( every person gets their phone back) = Pr (each person picks his phone ) multiplied by number of person
= [tex]\frac{1}{n}[/tex] × n = 1.
No of first m persons to pick = m
No of last m persons to pick = 1 - m
b) Pr (first m persons to pick each gets their phones back) = [tex]\frac{m}{n}[/tex]
c) Pr( first m persons get a phone belonging to last m persons) = [tex]\frac{1-m}{n}[/tex]
Traders often buy foreign currency in hope of making money when the currency's value changes. For example, on a particular day, one U.S. dollar could purchase 0.8869 Euros, and one Euro could purchase 143.1126 yen. Let fix) represent the number of Euros you can buy with x dollars, and let g(x) represent the number of yen you can buy with x Euros. (a) Find a function that relates dollars to Euros fx)Simplify your answer.) (b) Find a function that relates Euros to yen. gxSimplify your answer.) (c) Use the results of parts (a) and (b) to find a function that relates dollars to yen. That is, find (g o f)(x)-g(fx g(f(x)) Simplify your answer. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.) (d) What is g(1000))? g(f(1000)) Type an integer or decimal rounded to one decimal place as needed.)
Answers
Answer:
(a)f(x)=0.8869x
(b)g(x)=143.1126x
(c)g(f(x))=126.9266x
(d)g(f(1000))=126926.6 Yen
Step-by-step explanation:
Given on a particular day
One U.S. dollar could purchase 0.8869 EurosOne Euro could purchase 143.1126 yen(a)If x represents the number of Dollars
Since one can purchase 0.8869 Euro with 1 USD, the function f(x) is a direct relationship where x is dollars and f(x) is in Euros.
f(x)=0.8869x(b)If x represents the number of Euros
Since one can purchase 143.1126 yen with 1 Euros, the function g(x) is a direct relationship where x is Euros and g(x) is in Yen.
g(x)=143.1126x(c)Given:
g(x)=143.1126xf(x)=0.8869xg(f(x))=143.1126(0.8869x)
g(f(x))=126.9266x(d)g(f(1000))
g(f(x))=126.9266xg(f(1000))=126.9266 X 1000 =126926.6 Yen
Is 8 a solution to 3x + 9 = 13?
Answers
Answer:
No
Step-by-step explanation:
3x + 9 = 13
Subtract 9 from each side
3x + 9-9 = 13-9
3x = 4
Divide each side by 3
3x/3 = 4/3
x = 4/3
8 is not a solution
A study of 178 cases of disease X were identified from a state registry. A total of 220 control subjects were then recruited from random-digit dial procedure. 16 cases had been exposed, compared to only 8 controls. How likely were cases to report an exposure compared with controls
Answers
Answer:
2.47 times more likely.
Step-by-step explanation:
16 out of 178 cases were reported for exposure.
And 8 out of 220 control reported for exposure.
Chances that a case would be reported for exposure = (16/178) = 0.0898876404
Chances that one control would report for exposure = (8/220) = 0.0363636364
Comparing both, how likely were cases to report an exposure compared with controls
= (0.0898876404) ÷ (0.0363636364)
= 2.4719101085 = 2.47 times more likely.
Hope this Helps!!
f(-4) in the function f(x) = -2x - 3?
Answers
Answer:
5
Step-by-step explanation:
f(-4) f(x)=-2x-3
f(-4)=-2(-4)-3
f(-4)=8-3
f(-4)=5
Answer:
5
Step-by-step explanation:
you imput -4 for x then you proceed as normal solving the equation
-2(-4) - 3 since two negatives when multiplied make a positive
8 - 3
5
One month Isabel rented 5 movies and 2 video games for a total of$26 . The next month she rented 3 movies and 8 video games for a total of $53. Find the rental cost for each movie and each video game.
Answers
Answer:
a movie, m is 3
a video game, v is 5.5
Brainliest would be really appreciated. (need it to unlock chat)
Feel free to ask further questions if you feel like it.
Till then, have a nice day
Step-by-step explanation:
I 5m+2v=26
II 3m+8v=53
I 5m+2v=26 devide by 2 on both sides
5/2m+v=13 subtract 5/2m om both sides
v=13-5/2m
Now put this whole thing in the other equation II, replacing the v there
3m+8(13-5/2m)=53 just calculate it
3m+104-20m=53
-17m+104=53 subtract 53 on both sides
-17m+51=0 add 17m on both sides
51=17m devide by 17
3=m
we found m, v is easy
now put m in an equation from the start, let's take equation I here
I 5m+2v=26
5*(3)+2v=26
15+2v=26 subtract 15 on both sides
2v = 11 devide by 2
v = 5.5
So we found m and v, prices for single items. we can proof this when we put m and v into a given equation and the if it equals a true value
m & v in II
II 3m+8v=53
3*(3)+8*(5.5)=53
9+44=53
53=53
Seems legit.
To find the rental cost for each movie and video game, set up a system of equations based on the given information and solve for the variables.
Explanation:To find the rental cost for each movie and video game, we can set up a system of equations based on the given information.
Let's assign variables to represent the rental cost for each movie and video game. Let's use 'm' for the cost of a movie and 'g' for the cost of a video game.
Based on the first month's information, we can write the equation: 5m + 2g = 26
Based on the second month's information, we can write the equation: 3m + 8g = 53
Now we can solve this system of equations to find the values of 'm' and 'g'.
By solving the system of equations, we find that the rental cost for each movie is $4 and the rental cost for each video game is $5.
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Suppose each laptop of a certain type is assigned a series number, which consists of a sequenceof eight symbols: number, letter, letter, letter, number, number, number, number, where aletter is any one of 26 letters and a number is one among 0, 1,. . ., 9. Assume that all series numbers are equally likely.
(a) What is the probability that all symbols are different if one laptop is picked at random with equal probability?
(b) What is the probability that all symbols are different and the first number is the largest among the numbers?
Answers
Answer:
Step-by-step explanation:
There are 5numbers and 3 letters. Each number can be one among the 10 possible.
Each letter is 1 among the 26 available.
a)The number of possible unique serial numbers are
10^5x 26³
The number of 5 number combinations each different (order important) is 5!(10/5)= 30240
The number of 3 letter combinations each different (order important) is 3!(26/3)=15600
The required probability (that all symbols are different if one laptop is picked at random with equal probability) is
15600x3240/ 10^5x 26³=0.2684
b) The first letter must be at least 4 to be largest among the 5 numbers. So the first letter can be one of . 4,5,6,7,8,9..
The number of 5 number combinations each different and starting with 4 (order important) is .
4!=24
The number of 5 number combinations each different and starting with 5 (order important) is .
4!(5/4)= 120
The number of 5 number combinations each different and starting with 6 (order important) is .
4!(6/4)= 360
The number of 5 number combinations each different and starting with 7 (order important) is .
4!(7/4)= 840
The number of 5 number combinations each different and starting with 8 (order important) is
4!(8/4)= 1680
The number of 5 number combinations each different and starting with 9 (order important) is .
4!(9/4)= 3024
Thus, there are
The required probability ( that all symbols are different and the first number is the largest among the numbers) is
15600* 6040/10^5x 26³= 0.0537
simplified expression -6x+2/3(9-15x)-2
Answers
Answer:
-16x+4
Step-by-step explanation:
-6x+2/3(9-15x)-2
Distribute
-6x +2/3 *9 +2/3*(-15x) -2
-6x +6 -10x -2
Combine like terms
-6x-10x +6-2
-16x+4
The circle below represents one whole.
What percent is represented by the shaded area?
Answers
The region represented by the shaded area has 25% and accounts for one-quarter of the overall circle.
The area is the space occupied by any two-dimensional figure in a plane. The area of the circle is the space occupied by the circle in a two-dimensional plane.
The formula for calculating circle area is r2, where r is the radius of the circle.
The entire area of the circle in the accompanying figure is r2. The shaded area accounts for one-fourth of the circle's overall area.
Total area = πr²
Shaded area = ( 1 / 4 )πr²
The percentage of the shaded area will be calculated as
Shaded area = ( 1 / 4 )πr²
Shaded area = ( 0.25 )πr²
To convert it into a percentage multiply by 100.
Shaded area = ( 0.25 x 100 )πr²
Shaded area =25% πr²
Put πr² as the total area.
Shaded area =25% of Total area.
Therefore, the region represented by the shaded area has 25% and is 1/4th of the total circle.
7,945\100 Is the equal as which number?
Answers
Answer:
79.45
Step-by-step explanation:
Which prism has an area of 6 cubic units?
A prism has a length of 1 and one-half, height of 1, and width of 3.
A prism has a length of 2, height of 1 and one-half, and width of 2.
A prism has a length of 1 and one-fourth, height of 1, and width of 4.
A prism has a length of 3, height of 1 and one-fourth, and width of 2.
Answers
Answer:
A prism that has a length of 2, height of 1 and one-half, and width of 2.
Step-by-step explanation:
The formula for calculating the area of a prism is base area × height
Volume = L×W×H
L is the length of the prism
W is the width
H is the height.
To determine the prism that has an area of 6 cubic units, we will substitute the values in the option in the formula.
Using option D i.e prism that has a length of 2, height of 1 and one-half, and width of 2.
L = 2units, H = 1 1/2 units , W = 2units
Substituting in the formula for finding the volume
V = 2×2×3/2
Volume of the prism = 6cubic units
Answer:
B
Step-by-step explanation:
Can anyone help me please ASAP
Answers
Given:
It is given that the measurements of the triangle.
The measure of ∠2 is (3x + 3)°
The measure of ∠3 is (3x - 4)°
The measure of ∠4 is (5x + 8)°
We need to determine the measure of ∠1 and ∠4.
Value of x:
The value of x can be determined using the exterior angle theorem.
Applying the theorem, we have;
[tex]m \angle 4=m \angle 2+m \angle 3[/tex]
Substituting the values, we get;
[tex]5x+8=3x+3+3x-4[/tex]
[tex]5x+8=6x-1[/tex]
[tex]-x+8=-1[/tex]
[tex]-x=-9[/tex]
[tex]x=9[/tex]
Thus, the value of x is 9.
Measure of ∠4:
Substituting the value of x in the expression of ∠4, we get;
[tex]m\angle 4=5(9)+8[/tex]
[tex]=45+8[/tex]
[tex]m\angle 4=53^{\circ}[/tex]
Thus, the measure of ∠4 is 53°
Measure of ∠1:
The angles 1 and 4 are linear pairs and hence these angles add up to 180°
Thus, we have;
[tex]\angle 1+ \angle 4=180^{\circ}[/tex]
Substituting the values, we get;
[tex]\angle 1+ 53^{\circ}=180^{\circ}[/tex]
[tex]\angle 1=127^{\circ}[/tex]
Thus, the measure of ∠1 is 127°
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)
Answers
Answer:
In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.
In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.
In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.
Step-by-step explanation:
We have to write the transition matrix M for the population.
We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.
We can write the transition matrix, in which the rows are the actual state and the columns are the future state.
- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. Then, the probability of staying in the same state is 90%.
- For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. Then, the probability of staying in the same state is 80%.
- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. Then, the probability of staying in the same state is 82%.
The transition matrix becomes:
[tex]\begin{vmatrix} &NS&P1&PM\\NS& 0.90&0.08&0.02 \\ P1&0.10&0.80 &0.10 \\ PM& 0.08 &0.10&0.82 \end{vmatrix}[/tex]
The actual state matrix is
[tex]\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right][/tex]
We can calculate the next month state by multupling the actual state matrix and the transition matrix:
[tex]\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right][/tex]
In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.
To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:
[tex]\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right][/tex]
In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.
If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:
[tex]\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right][/tex]
In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.
A student takes a true-false test that has 10 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(Fewer than 3). Round your answer to 2 decimal places.
Answers
Answer:
P(Fewer than 3) = 0.05.
Step-by-step explanation:
We are given that a student takes a true-false test that has 10 questions and guesses randomly at each answer.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 10 questions
r = number of success = fewer than 3
p = probability of success which in our question is probability
that question is answered correctly, i.e; 50%
LET X = Number of questions answered correctly
So, it means X ~ Binom(n = 10, p = 0.50)
Now, Probability that Fewer than 3 questions are answered correctly is given by = P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0}+ \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1}+ \binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}[/tex]
= [tex]1 \times 0.50^{10} + 10 \times 0.50^{10} +45 \times 0.50^{10}[/tex]
= 0.05
Hence, the P(Fewer than 3) is 0.05.
To find the probability of the student passing the test with at least a 70 percent, we can use the binomial probability formula. The probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).
Explanation:To find the probability of the student passing the test with at least a 70 percent, we need to find the probability of the student answering 7, 8, 9, or 10 questions correctly out of the 10 questions. Since the student randomly guesses at each answer, the probability of guessing correctly is 0.5. Now we can calculate the probability using the binomial probability formula:
P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
P(X = k) = C(10, k) * (0.5)^k * (0.5)^(10-k), where C(n, r) is the binomial coefficient (n choose r).
Calculating each probability and summing them up, we get P(X ≥ 7) = 0.171875. Therefore, the probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).
A certain drug is used to treat asthma. In a clinical trial of the drug, 23 of 277 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 10% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below.
a. What is test statistic?
b. What is p-value?
c. What is the null hypothesis, and what can we conclude about it?
d. Decide whether to reject the null hypothesis?
e. What is the final conclusion?
Answers
Answer:
a) The test statistic is z=-0.94
b) The p-value is 0.1736
c) The null hypothesis is [tex]H_0:p=0.10[/tex], we can conclude that, if the result is not significant at 0.01 level, we fail to reject the null hypothesis
d) We fail to reject the null hypothesis at 0.01 significance level.
e) We do not have sufficient evidence to reject the claim that, less than 10% of the treated subjects experienced headaches.
Step-by-step explanation:
The test statistic is defined by:
[tex]Z=\frac{\hat p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]
It was given that, 23 of 277 treated in the clinical trial of the drug subjects experienced headaches.
This means that:
[tex]\hat p=\frac{23}{277}\approx 0.083[/tex] and n=277
The claim is that, less than 10% of treated subjects experienced headaches. This means:
[tex]p_0=\frac{10}{100}=0.1[/tex]
We substitute the values into the formula to obtain:
[tex]Z=\frac{0.083-0.1}{\sqrt{\frac{0.1(1-0.1)}{277} } }[/tex]
The test statistics becomes:
[tex]Z=-0.94[/tex]
b) From the normal distribution table, the p-value corresponds to Z=-0.94 .
Since this is a left-tailed test, the p-value corresponds to area under the normal curve that is to the left of z=-0.94
P(Z<-0.94)=0.173609.
c) Since the claim is that, less than 10% of treated subjects experienced headaches, the null hypothesis is
[tex]H_0:p=0.10[/tex]
The alternate hypothesis will be:
[tex]H_1:p\:<\:0.10[/tex]
This implies that, the result is not significant at 0.01 alpha level.
d) We need to compare the p-value to the significance level. If the significance level is greater than the null hypothesis, we reject the null hypothesis.
Since 0.01<0.1736, we fail to reject the null hypothesis.
d) Conclusion: There is no enough evidence to reject the claim that, less than 10% of treated subjects experienced headaches.
Answer:
(a)Test statistic[tex]z_{score}=-0.94[/tex]
(b) p-value=0.1736
(c)Null hypothesis,
[tex]H_0:p=0.10[/tex]
(d)[tex]\alpha>p[/tex], we reject the null hypothesis.
(e)We have experimental values to reject the claim.
Step-by-step explanation:
Given information;
n=277
Significance level [tex]\alpha[/tex]=0.01
By normal distribution,
[tex]z_{score}=\frac{\widehat{p}-p_0}{\frac{\sqrt {p_0(1-p_0)}}{n}}[/tex]
[tex]\widehat{p}=\frac{23}{277}=0.83[/tex]
[tex]p_0=10[/tex]%=0.1
On substitution,
[tex]z_{score}=\frac{{0.83}-0.1}{\frac{\sqrt {0.1(1-0.1)}}{277}}[/tex]
Test static,
[tex]z_{score}=-0.94[/tex]
b)From the table normal distribution,
for,[tex]z_{score}=-0.94,[/tex]
[tex]P(z<-0.94)=0.173609[/tex]
(c)Null hypothesis,
[tex]H_0:p=0.10[/tex]
Alternate hypothesis,
[tex]H_1:p<0.10[/tex]
It implies result is not significant at
[tex]\alpha=0.01[/tex]
(d) On compare value if
[tex]\alpha>p[/tex], we reject the null hypothesis.
For more details please refer link:
https://brainly.com/question/5286270?referrer=searchResults
Find the volume of the figure.
2.25 m
4
m
2.5 m
no
Answers
Given:
Given that the figure is a triangular prism.
The length of the prism is 4 m.
The base of the triangle is 2.5 m.
The height of the triangle is 2.25 m.
We need to determine the volume of the triangular prism.
Volume of the triangular prism:
The volume of the triangular prism can be determined using the formula,
[tex]V=\frac{1}{2}bhl[/tex]
where b is the base of the triangle,
h is the height of the triangle and
l is the length of the prism.
Substituting b = 2.5, h = 2.25 and l = 4 in the above formula, we get;
[tex]V=\frac{1}{2}(2.5)(2.25)(4)[/tex]
[tex]V=\frac{1}{2}(22.5)[/tex]
[tex]V=11.25 \ m^3[/tex]
Thus, the volume of the triangular prism is 11.25 m³
Round your answer to the nearest hundredth. Again.
Answers
Given:
In the given triangle ΔABC,
AB = 9 unit
AC = 2 unit
To find the value of ∠ABC.
Formula
From trigonometric ratio we get,
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
Let us take, ∠ABC = [tex]\theta[/tex]
With respect [tex]\theta[/tex], AC is the opposite side and AB is the hypotenuse.
So,
[tex]sin \theta = \frac{AC}{AB}[/tex]
or, [tex]sin \theta[/tex] = [tex]\frac{2}{9}[/tex]
or, [tex]\theta = sin^{-1} (\frac{2}{9} )[/tex]
or, [tex]\theta= 12.84^\circ[/tex]
Hence,
The value of ∠ABC is 12.84°.
Which of the following are examples of limiting factors?
food, water, cell composition
cell composition water sunlight
food water sunlight
sizer water sunlight
Answers
examples of limiting factors are, food, water and sunlight
Find the slope
(-19,-6) (15,16)
Answers
Answer:
11/17
Step-by-step explanation:
slope between two points: slope = (y2 - y1) / (x2 - x1)
(x1, y1) = (-19, -6), (x2, y2) = (15, 16)
m = (16 - ( - 6)) / (15 - ( - 19))
refine
m = 11/17
sorry it is hard to follow... i am on my phone rn :/
Final answer:
The slope between the points (-19, -6) and (15, 16) is 11/17.
Explanation:
To find the slope of the line connecting the points (-19,-6) and (15,16), we will use the slope formula which is the change in y-coordinates divided by the change in x-coordinates. Here is the process:
Identify the coordinates of the two points. Point 1 is (-19, -6), and Point 2 is (15, 16).Apply the slope formula: m = (y2 - y1) / (x2 - x1).Substitute the given values into the formula: m = (16 - (-6)) / (15 - (-19)) = (16 + 6) / (15 + 19).Simplify: m = 22 / 34.Reduce to the simplest form: m = 11 / 17.Therefore, the slope of the line connecting the two points is 11/17.
8. Lara subtracts 73 from 188. Which one of these
steps should she follow?
o Ungroup 8 tens as 7 tens 10 ones.
o Subtract 3 ones from 8 tens.
o Subtract 7 tens from 8 tens.
Answers
Answer: o Subtract 7 tens from 8 tens.
Step-by-step explanation: you subtract
Answer:
Step-by-step explanation:subtract 7 tens from 8 tens
Deandre just bought 9 bags of 15 cookies each. He already had 6 cookies in a jar. How many cookies does deandre have now?
Answers
Answer:
141 cookies
Step-by-step explanation:
amount of cookies
= 9(15) + 6
= 135 + 6
= 141
What is the volume of the following rectangular prism
Answers
Answer:
7 2/3
Step-by-step explanation:
Multiply 4/3 by 23/4