Answer:
a) 60% probability that student took at least one online course
b) 40% probability that student did not take an online course
c) 12.96% probability that all 4 students selected took online courses.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they took at least one online course last fall, or they did not. The probability of a student taking an online course is independent of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
3 out of 5 students enrolled in higher education took at least one online course last fall.
This means that [tex]p = \frac{3}{5} = 0.6[/tex]
a) If you were to pick at random 1 student enrolled in higher education, what is the probability that student took at least one online course?
This is P(X = 1) when n = 1. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{1,1}.(0.6)^{1}.(0.4)^{0} = 0.6[/tex]
60% probability that student took at least one online course.
b) If you were to pick at random 1 student enrolled in higher education, what is the probability that student did not take an online course?
This is P(X = 0) when n = 1.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{1,1}.(0.6)^{0}.(0.4)^{1} = 0.4[/tex]
40% probability that student did not take an online course
c) Now, consider the scenario that you are going to select random select 4 students enrolled in higher education. Find the probability that all 4 students selected took online courses
This is P(X = 4) when n = 4.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]
12.96% probability that all 4 students selected took online courses.
indicate below whether the equation in the box is true or false.
Answer:
True
Step-by-step explanation:
Multiply the top the same as the bottom
6*2=12
10*2=20
Answer:
The answer is true.
Step-by-step explanation:
6/10 = 12/20 because if you multiply 2 to the numerator and the denominator of 6/10, then the resulting fraction is 12/20. Because 12/20 = 12/20, the answer is true.
Integral cos(3x)^3sen(3x)^7dx
One way to do this is to exploit the Pythagorean identity,
[tex]\cos^2x+\sin^2x=1[/tex]
to rewrite
[tex]\cos^3(3x)=\cos(3x)\cos^2(3x)=\cos(3x)(1-\sin^2(3x))[/tex]
so that
[tex]\displaystyle\int\cos^3(3x)\sin^7(3x)\,\mathrm dx=\int\cos(3x)\left(\sin^7(3x)-\sin^9(3x)\right)\,\mathrm dx[/tex]
Then substitute [tex]u=\sin(3x)[/tex] and [tex]\frac{\mathrm du}3=\cos(3x)\,\mathrm dx[/tex] to get the integral
[tex]\displaystyle\frac13\int u^7-u^9\,\mathrm du=\frac13\left(\frac{u^8}8-\frac{u^{10}}{10}\right)+C[/tex]
[tex]=\boxed{\dfrac{\sin^8(3x)}{24}-\dfrac{\sin^{10}(3x)}{30}+C}[/tex]
which is one correct form of the antiderivative. There's no reason we can't use the identity from before to express the integrand in terms of powers of cos(3x) instead.
Keep gettin this wrong please help!!!
Answer:
none of the options shown
Step-by-step explanation:
You can add 2x+2 to the inequality and get ...
8 ≥ 2x
4 ≥ x . . . . . divide by 2
This means that there should be a solid circle at x=4, and shading should be to the left of that.
None of the three graphs shown here is appropriate. (We don't see Option 2.)
__
Attached is the output of a graphing calculator. The solid line at x=4 corresponds to a filled dot on a number line plot.
Convert the angle 0=100 degrees to radians. What’s the exact answer??
Find and interpret the mean absolute deviation of the data. Round your answers to the nearest tenth. If necessary 101.5 98.7 95.4 92.3 109.8 104.7
Answer:
[tex]\bar X = 100.4[/tex]
And we can calculate the deviations from each value like this:
[tex] |101.5-100.4 |=1.1[/tex]
[tex] |98.7-100.4 |=1.7[/tex]
[tex] |95.4-100.4 |=5.0[/tex]
[tex] |92.3-100.4 |=8.1[/tex]
[tex] |109.8-100.4 |=9.4[/tex]
[tex] |104.7-100.4|=4.3[/tex]
And the mean absolute deviation would be:
[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
101.5 98.7 95.4 92.3 109.8 104.7
We can calculate the mean with the following formula:
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X = 100.4[/tex]
And we can calculate the deviations from each value like this:
[tex] |101.5-100.4 |=1.1[/tex]
[tex] |98.7-100.4 |=1.7[/tex]
[tex] |95.4-100.4 |=5.0[/tex]
[tex] |92.3-100.4 |=8.1[/tex]
[tex] |109.8-100.4 |=9.4[/tex]
[tex] |104.7-100.4|=4.3[/tex]
And the mean absolute deviation would be:
[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]
"If a circle has diameter 10 units, what is its circumference? What is its area?
What is the equation of the following line written in slope intercept form
Answer:
The equation can be y = -7x+11
Please answer this correctly
Answer:
9.5 ft
Step-by-step explanation:
The perimeter is equal to
P =2(l+w)
29.6 = 2(5.3+z)
Divide each side by 2
29.6 /2 =2/2(5.3+z)
14.8 = 5.3 +z
Subtract 5.3 from each side
14.8-5.3 = z
9.5 =z
Answer:
Z=9.5
Step-by-step explanation:
Perimeter(of a triangle)=2(5.3+z)
29.6=10.6+2z
2z=29.6-10.6
2z=19(then divide both sides by 2 to find the value of z)
z=19/2
z=9.5 ft
To check your answer
29.6=2(5.3+9.5)
29.6=2(14.8)
29.6=29.6 so your answer is correct.
In finance, one example of a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage in a certain bundle has a probability of 0.08 of default. (a) What is the probability that a randomly selected mortgage will not default? (b) What is the probability that nine randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the others? Note: A derivative might be an investment that only pays when all nine mortgages do not default. (c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of the mortgages defaults
Answer:
a) 92% probability that a randomly selected mortgage will not default
b) 47.22% probability that nine randomly selected mortgages will not default
c) 52.78% probability that the derivative from part (b) becomes worthless
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening
Suppose a randomly selected mortgage in a certain bundle has a probability of 0.08 of default.
This means that [tex]p = 0.08[/tex]
(a) What is the probability that a randomly selected mortgage will not default?
Either it defaults, or it does not default. The sum of the probabilities of these outcomes is 1. So
0.08 + p = 1
p = 0.92
92% probability that a randomly selected mortgage will not default
(b) What is the probability that nine randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the others?
This is P(X = 0) when n = 9. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{9,0}.(0.08)^{0}.(0.92)^{9} = 0.4722[/tex]
47.22% probability that nine randomly selected mortgages will not default.
(c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of the mortgages defaults
Either none defect, or at least one does. The sum of the probabilities of these events is 100%. So
p + 47.22 = 100
p = 52.78
52.78% probability that the derivative from part (b) becomes worthless
A parking lot for a new ice cream stand has an area of 5000 square yards. The length of the lot is 50 yards longer than its width. Determine algebraically the dimensions of the parking lot, in yards.
Answer:
length = 50 + 50 = 100 yards
width = 50 yards
Step-by-step explanation:
The area of parking lot for the the ice cream stand is given as 5000 yard². The length of the yard is 50 yard longer than its width.
Let
width = a
length = 50 + a
The parking lot is definitely a rectangle .
Area of a rectangle = length × width
area = (50 + a)a
5000 = (50 + a)a
5000 = 50a + a²
a² + 50a - 5000 = 0
The numbers that can be multiply together to give you -5000 is -50 and 100 and this same number can be added to give 50. Therefore,
a² - 50a + 100a - 5000 = 0
a(a - 50) + 100(a - 50) = 0
(a + 100)(a - 50) = 0
a = -100 or 50
We can't use negative value so we use 50.
length = 50 + 50 = 100 yards
width = 50 yards
A Broadway theater has 800 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $ 40 comma main seats for $ 30 comma and balcony seats for $ 20. If all the seats are sold, the gross revenue to the theater is $ 23 comma 200. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 20 comma 000. How many are there of each kind of seat?
orchestra seats: main seats: balcony seats:
Answer:
orchestra seats: main seats: balcony seats: 160: 400: 240
Step-by-step explanation:
Let number of orchestra seats = x
Let number of main seats = y
Let number of balcony seats = z
As per given statement, total seats are 800
[tex]x +y+z=800 ..... (1)[/tex]
Sales price of each orchestra seat = $40
Sales price of each main seat = $30
Sales price of each balcony seat = $20
If all the seats are sold, total revenue is $23200.
[tex]\Rightarrow 40x + 30y+20z=23200 ...... (2)[/tex]
If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 20 comma 000.
[tex]\Rightarrow 40\times \dfrac{x}{2} + 30y+20z=20000\\\Rightarrow 20x + 30y+20z=20000 ...... (3)[/tex]
Here, we have 3 variables and 3 equations. Let us solve them.
Subtracting Equation (3) from equation (2):
[tex]\Rightarrow 20x = 3200\\\Rightarrow x = 160[/tex]
Putting value of x in equations (1) and (2):
Equation (1)
[tex]\Rightarrow 160 +y+z=800\\\Rightarrow y+z=640 ...... (4)[/tex]
Equation (2)
[tex]\Rightarrow 40\times 160 +30y+20z=23200\\\Rightarrow 30y+20z=16800\\\Rightarrow 3y +2z=1680 ...... (5)[/tex]
Equation (5) - 2 [tex]\times[/tex] Equation(4):
[tex]\Rightarrow y =400[/tex]
Putting value of y in equation (4):
[tex]400 +z = 640\\\Rightarrow z =240[/tex]
Hence, answer is:
orchestra seats: main seats: balcony seats: 160: 400: 240
Esmerelda is a home healthcare provider. When she takes a new client, she charges an initial fee of $32 and an hourly fee of $16 per hour. Her last new client paid her $144. How many hours did Esmerelda work for her new client?
Question 31 pts Prove the statement is true using mathematical induction: 2n-1 ≤ n! Use the space below to write your answer. To make the < symbol, you might want to use the < with the underline feature.
Answer:
P(3) is true since 2(3) - 1 = 5 < 3! = 6.
Step-by-step explanation:
Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3
Basis: P(3) is true since 2(3) - 1 = 5 < 3! = 6.
Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:
2(k+1) - 1 = 2k + 2 - 1
≤ 2 + k! (by the inductive hypothesis)
= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.
8. What is the value of x?
Answer:
16
Step-by-step explanation:
The midpoint theorem says that if a line bisects the two sides of the triangle , it is parallel to the third side and half of it
Thus the x = 1/2 × 32 = 16
Determine which statements are true in the set of real numbers3. (Select all that apply.) (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a third plane are parallel. (d) Two planes perpendicular to a third plane are parallel. (e) Two lines parallel to a plane are parallel. (f) Two lines perpendicular to a plane are parallel. (g) Two planes parallel to a line are parallel. (h) Two planes perpendicular to a line are parallel. (i) Two planes either intersect or are parallel. (j) Two lines either intersect or are parallel. (k) A plane and a line either intersect or are parallel. Incorrect: Your answer is incorrect.
Answer:
(a) True
(b) False
(c) True
(d) False
(e) False
(f) True
(g) False
(h) True
(i) True
(k) True
Step-by-step explanation:
(a) Two lines parallel to a third line are parallel
True
(b) Two lines perpendicular to a third line are parallel
Only for lines on the same plane
Therefore, false
(c) Two planes parallel to a third plane are parallel
True
(d) Two planes perpendicular to a third plane are parallel
The two planes can be at an angle to each other and so intersect
Therefore, false
(e) Two lines parallel to a plane are parallel
Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect
Therefore, false
(f) Two lines perpendicular to a plane are parallel
True
(g) Two planes parallel to a line are parallel
Where the planes are not parallel to each other, they will intersect
Therefore, false
(h) Two planes perpendicular to a line are parallel
True
(i) Two planes either intersect or are parallel
True
(k) A plane and a line either intersect or are parallel
True.
Si la medida de la circunferencia de una glorieta es de 70 m, ¿cuanto mide su diametro?
Diameter of round bud is 22.29 m.
Given that,
The circumference of round bud = 70 m
We have to calculate its diameter,
Since we know that,
Its shape is circular,
Since,
The circumference of the circle, also known as the perimeter of the circle, is the measurement of the circle's boundary. The area of a circle, on the other hand, specifies the territory it occupies. If we open a circle and draw a straight line through it, the length of the line equals the circumference.
S,
⇒ Circumference = 2πr
Where r is radius of circle,
⇒ 70 = 2πr
⇒ r = (70/2x3.14)
⇒ r = 11.14
Here we know that,
Diameter = 2r
Hence,
Diameter = 22.29 m
To learn more about circle visit:
https://brainly.com/question/29288238
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A researcher wanted to determine the effectiveness of a new cream in the treatment of warts. She identified 145 individuals who had two warts. She applied cream A on one wart and cream B on the second wart. Test whether the proportion of successes with cream A is different from cream B at the alpha equals 0.05 level of significance. Treatment ATreatment B Success Failure Success 61 11 Failure 21 52(a) What type of test should be used? A. A hypothesis test regarding the difference of two means using a matched-pairs design B. A hypothesis test regarding the difference between two population proportions from dependent samples C. A hypothesis test regarding two population standard deviations D. A hypothesis test regarding the difference between two population proportions from independent samples (b) Determine the null and alternative hypotheses. A. H0 : p1 = p2, H1 : p1 >p2B. H0 : p1 < p2, H1 : p1 >p2C. H0 : p1 = p2, H1 : p1
Answer:
a. Option D
b. H₀ : p₁ = p₂, H₁: p1 ≠ p₂
Step-by-step explanation:
a. A hypothesis test regarding the difference between two population proportions from independent samples. This type of test is used to compare the proportions of two populations. This test is usually appropriate under the conditions that:
The sampling method for each population is simple random sampling.
The samples are independent.
Each sample includes at least 10 successes and 10 failures.
Each population is at least 20 times as big as its sample.
b. Null hypothesis: H₀ : p₁ = p₂
Alternative hypothesis: H₁ : p₁ ≠ p₂
What’s the correct answer for this question ?
Answer:
B:
Step-by-step explanation:
P(A or B) = P(A)+P(B)-P(A and B)
0.5 = 0.4 + P(B) -0.2
P(B) = 0.5-0.4+0.2
P(B) = 0.3
Solve the system of equations. 5x + 3y = 4 2x + y = 1
Answer:
(-1, 3)
Step-by-step explanation:
5x + 3y = 4
2x + y = 1 ⇒ y=1-2x
5x+3(1-2x)=45x+3-6x=4-x=4-3-x=1x=-1y= 1-2(-1)= 1+2=3Factor 1
Use algebra tiles to represent this polynomial: x2 -5x - 1
Product
Step 1: Drag one xtile to the section labeled Product.
Factor 2
Check
Answer:
See explanation and attachment.
Step-by-step explanation:
One of the ways to represent polynomial is the use of algebraic tiles.
To represent the polynomial x²-5x-1, we would use algebraic tiles to represent each of the three terms.
Algebra tiles come with different colors and sizes. Each size is equivalent to a degree of different monomials.
The x² tile is a monomial with degree of 2, the x tile is a monomial with degree of 1 and the unit tile (constant) is a monomial with degree of 0.
Let the shaded tiles represent the positive tiles and the unshaded tile represent the negative tiles.
Find attached the diagram for the tiles.
To represent the polynomial x² - 5x - 1, we would need 1 shaded x² tile, 5 unshaded x tiles and 1 unshaded unit tile. Then we would arrange the tiles to correspond with the polynomial.
Answer:
Answer:
(drag one tile) +x 2 into the product then click check.
(drag five) -x into the product then click check.
(drag one) - tile into the product and click check..
Step-by-step explanation:
At a financial services company, the mean percent allocation for bonds in a retirement portfolio is 26.9 percent with a population standard deviation of 3.6 percent. A random sample of 35 retirement plan participants was taken and the probability that the mean bond percent for the sample will be at least 28 percent was determined. Was the probability a Left-tail, Right -tail or Interval Probability
Answer: it is a right tailed probability
Step-by-step explanation:
Population proportion = 26.9/100 = 0.269
We are dealing with the fact that the probability that the mean bond percent for the sample will be at least 28. This means that the sample proportion is 0.28 or above. This means that it is greater than the population proportion of 0.269
The hypothesis would be
For null hypothesis
p = 0.269
For alternative hypothesis,
p > 0.269
The inequality sign means that it is right tailed.
A carpenter had a piece of wood that was 15 feet in length. If he needs only 10 &five twelfth feet of wood, then how much wood should he cut ?
Answer:
12.5 feet
Step-by-step explanation:
He only needs 10/12 of a 15 foot long piece of wood. We need to find 10/12 of the length of the wood.
That is:
10/12 * 15 = 12.5 feet
He only needs 12.5 feet of the piece of wood.
Write an expression to represent: Four less than the quotient of a number xxx and 555.
Answer:
4/r -1
Step-by-step explanation:
i did khan
but sorry if its pooop
Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3times3 determinants. [Note: Finding the characteristic polynomial of a 3times3 matrix is not easy to do with just row operations, because the variable lambda is involved.]
Answer:
Step-by-step explanation:
Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3times3 determinants. [Note: Finding the characteristic polynomial of a 3times3 matrix is not easy to do with just row operations, because the variable lambda is involved.]
[tex]\texttt {let} A = \left[\begin{array}{ccc}4&-4&0\\-4&7&0\\4&6&5\end{array}\right][/tex]
The characteristics polynomial of A is [tex]|A- \lambda I|[/tex]
[tex]\to|A-\lambda I|=\left[\begin{array}{ccc}(4-\lambda)&-4&0\\-4&(7-\lambda)&0\\4&6&(5-\lambda)\end{array}\right][/tex]
[tex]=(4-\lambda)[7-\lambda)(5-\lambda)-0]+4[-4(5-\lambda)-0]+0[-4\time 6-4(7-\lambda)]\\\\=(4-\lambda)[35-7\lambda-5\lambda+\lambda^2]+4[-20+4\lambda]+0\\\\=(4-\lambda)[35-12\lambda+\lambda^2]-80+16\lambda\\\\=140-48\lambda+4\lambda^2-35\lambda+12\lambda^2-\lambda^3-80+16\lambda\\\\=-\lambda^3+16\lambda^2-67\lambda+60[/tex]
What is 6 1/3-2 1/4 as a fraction?
Answer:
[tex]49/12[/tex]
Step-by-step explanation:
[tex]6\frac{1}{3} -2\frac{1}{4}[/tex]
[tex]\frac{19}{3} -\frac{9}{4}[/tex]
[tex]\frac{49}{12}[/tex]
Answer:
4 1/12
Step-by-step explanation:
6 1/3 - 2 1/4
Get a common denominator of 12
6 1/3*4/4 - 2 1/4*3/3
6 4/12 - 2 3/12
4 1/12
Help asap GIVING BRANLIST!!!!
Answer:
The first graph
Step-by-step explanation:
when x is equal to something it is always up
y = 2 would be #4
Answer:
The first graph
Step-by-step explanation:
Personally, I use the acronym HAY and VAX to remember this rule. This means that horizontal lines always correlate with y and vertical lines always correlate with x. A horizontal equation (y=#) is valid, so to say, whereas vertical (x=#) is undefined. It is undefined because there are multiple values of y for the same value of x. You can remember this with the following scenario: A person will always be able to walk in a straight line without getting injuries, but if a person tries to walk up the wall, they will fall and can break their bones, making their body "undefined"
Enter a positive common factor (other than 1) of 15 and 10
On average, the parts from a supplier have a mean of 31.8 inches and a standard deviation of 2.4 inches. Find the probability that a randomly selected part from this supplier will have a value between 27.0 and 36.6 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?
Answer:
The probability is P=0.9545.
The empirical rule is consistent, as it would have estimate a probability of 95%.
Step-by-step explanation:
We have a random variable with mean 31.8 in. and standard deviation of 2.4 in.
We have to find the probability that a randomly selected part from this supplier will have a value between 27.0 and 36.6 in.
If we assumed a normal-like distribution, we can calculate the z-score for both values:
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{27-31.8}{2.4}=\dfrac{-4.8}{2.4}=-2\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{36.6-31.8}{2.4}=\dfrac{4.8}{2.4}=2[/tex]
That can be interpreted as an interval that is 2 standard deviations wide, centered on the mean.
This interval has a probability of:
[tex]P(27.0<x<36.6)=P(-2<z<2)=0.9545[/tex]
If we apply the empirical rule, with 2 standard deviations from the mean, we would have estimate a probability of 95%, which is accurate.
What’s the correct answer for this?
Find the probability of each one:
Taffy would be 1/6
Chips would be 1/3
Soda would be 1/3
For the probability of all three multiply them together:
1/6 x 1/3 x 1/3 = 1/54
Samantha and Jillian were going for a walk. Jillian left 15 seconds ahead of Samantha. Samantha walked at a speed of 7 feet per second.Jillian walked at a speed of 6 feet per second. How many seconds had Jillian been walking when the two girls had walked the same distance?
Answer:
105 seconds
Step-by-step explanation:
We can use the relation ...
distance = speed · time
to write equations for the distance each girl travels as a function of time t since Jillian started.
Jillian's distance = (6 ft/s)(t)
Samantha's distance = (7 ft/s)(t -15) . . . . Samantha starts 15 seconds after the clock starts running
These distances are the same when ...
6t = 7(t -15)
6t = 7t -105 . . . . eliminate parentheses
105 = t . . . . . . . . add 105-6t
Jillian had been walking 105 seconds when the two girls met.