Answer:
The probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.
Step-by-step explanation:
We have a cube, with the faces painted black, that each side is divided in 5, so we end up with 125 cubes.
We have to calculate the probability that a randomly selected cube is rolled and the face on the top is black.
This probability is equal to the proportion of black area in the total area of the cube.
We can define the side of the original cube as A=5a, being a the side of the small cubes.
The area that is painted black is equal to the sum of 6 squares of side A. In terms of a, that is:
[tex]S_b=6\cdot A^2=6\cdot(5a)^2=6\cdot25a^2=150a^2[/tex]
The total area of the 125 small cubes is:
[tex]S=125(6a^2)=750a^2[/tex]
Then, the ratio of black surface to the total surface is:
[tex]s_b/s=(150a^2)/(750a^2)=0.2[/tex]
Then, we can conclude that the probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.
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
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.
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]
HELPPPPP
Lisa is framing a rectangular painting length more than twice the widthShe uses 30 inches of framing material. What the length of the paintingWrite equation and solve.
A.3w+3=30;21
b.3w+3=30;9
C.6w+6=30;11
D.6w + 6 = 30 = 4
Answer:
6w = 30
Step-by-step explanation:
We should know that the 30 inches of framing material were used to frame the four sides of the rectangle.
The perimeter of the rectangle is what we should be considering, whenever we are dealing with frames.
This is 2 X (length + width)
From the questions, we can get the dimensions of the rectangle using clues from the various statements made.
From the statement"a rectangular painting length more than twice the width" we can see that the
L = 2w ------------------------- equation 1
substituting this value into the formula for the perimeter of the rectangle we have
30 = 2(2w + w)
30 = 6w
w= 5
from equation 1
L =2 X (5) = 10
Hence, we can set up the equation
6w = 30
However, the closest option to what we have is option D
6w + 6 = 30 - 4
complete question:
Lisa is framing a rectangular painting. The length is three more than twice the width. She uses 30 inches of framing material. What is the length of the printing? Write an equation and solve
Answer:
D.6w + 6 = 30 = 4
Step-by-step explanation:
perimeter = 30 inches
width = w
length = 2w + 3
perimeter of a rectangle = 2l + 2w
where
w = width
l = length
Therefore,
perimeter of a rectangle = 2(2w + 3) + 2w
perimeter of the rectangle = 4w + 6 + 2w
perimeter = 6w + 6
recall
perimeter = 30 inches
6w + 6 = 30
6w = 24
divide both sides by 6
w = 24/6
w = 4
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.
Please answer this correctly. I want genius,expert and ace people to answer this correctly as soon as possible as my work is due today
Answer:
50%
Step-by-step explanation:
27 to 30 is exactly the "box" of the box plot and that, by definition, contains 50% of the results.
Answer:
50%
Step-by-step explanation:
Hope this will help
Enter a positive common factor (other than 1) of 15 and 10
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.
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
n a basket of fruit, 5/6 of the pieces of fruit are apples. There are 20 apples in the display. The equation 5/6f= 20 can be used to find how many pieces of fruit f are the basket. Use words and numbers to explain how to solve the equation to find how many pieces of fruit are in the basket.
Step-by-step explanation:
5/6f=20apples. that means the total number of fruits is 6/6 which is whole thus
if 5/6=20
6/6=?
that is 6/6x20 divide by 5/6
=24fruits
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.
Convert the angle 0=100 degrees to radians. What’s the exact answer??
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
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]
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?
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.
What is the equation of the following line written in slope intercept form
Answer:
The equation can be y = -7x+11
I need help with this question ???
Answer:
i dont know how many decimals you need but its 5.56
tell me if u want an explanation
Answer:
5.74456264654
Step-by-step explanation:
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.
"If a circle has diameter 10 units, what is its circumference? What is its area?
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
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=3Write 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
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.
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.
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
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"
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
#SPJ2
What’s the correct answer for this question?
Answer:
Arc length : In his pizza, Arc length is the outer boundary of pizza and it can be calculated if we know the side length of the pizza and the central angle
Area of sector: since the whole pizza piece is a sector hence to calculate it's area we can use the formula of area of sector
(In degrees) = m/360 (πr²)
(In radians) = 1/2r²∅(theta)
