Answer:
1/6
Step-by-step explanation:
When a die is rolled twice the possible outcomes are:
Here the first value represents the first outcome and the second value represents the second outcome.
S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3),(2,4), (2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6), ( 4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)}
Total outcomes = n(S) = 36
Let A be the event that the sum of both outcomes is 7.
A = {(1, 6) , (2,5), (3,4) , (4,3), (5,2), (6,1)}
n(A) = 6
So, P(A) = n(A)/n(S)
= 6/36
= 1/6
In this scenario, there are 36 potential outcomes when rolling a die twice. Six of these outcomes would lead to a sum of 7. Therefore, the probability of rolling two numbers whose sum is 7 is 1/6.
Explanation:When rolling a single six-sided die twice, the sample space consists of 36 outcomes (since each roll can result in one of six possible outcomes, so 6 outcomes for the first roll times 6 outcomes for the second roll gives 36 total). Now, we need to find the probabilities that would result in a sum of 7. These are: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1. These are 6 possible outcomes. Hence, the probability of getting the two numbers whose sum is 7 is 6 out of 36, or 1/6 when simplified.
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Box 1 contains 1000 lightbulbs of which 10% are defective. Box 2 contains 2000 lightbulbs of which 5% are defective. (a) Suppose a box is given to you at random and you randomly select a lightbulb from the box. If that lightbulb is defective, what is the probability you chose Box 1? (b) Suppose now that a box is given to you at random and you randomly select two light- bulbs from the box. If both lightbulbs are defective, what is the probability that you chose from Box 1? 4 Solve the Rainbow
Answer:
a) There is a 66.7% chance that you were given box 1
b) There is a 80% chance that you were given box 1
Step-by-step explanation:
To find this, we need to note that there is a 1/10 chance of getting a defective bulb with box 1 and a 1/20 chance in box 2.
a) To find the answer to this, find the probability of getting a defective bulb for each box. Since there is only one bulb pulled in this example, we just use the base numbers given.
Box 1 = 1/10
Box 2 = 1/2
From this we can see that Box 1 is twice as likely that you get a defective bulb. As a result, the percentage chance would be 2/3 or 66.7%
b) For this answer, we need to square each of the probabilities in order to get the probability of getting a defective one twice.
Box 1 = 1/10^2 = 1/100
Box 2 = 1/20^2 = 1/400
As a result, Box 1 is four times more likely. This means that it would be a 4/5 chance and have a probability of 80%
The solution involves using conditional probability and Bayes' theorem to find the chance of picking a defective lightbulb from a specific box. In part (b), the problem is slightly more complex, assuming the lightbulbs are selected independently.
Explanation:This problem involves conditional probability. We're given two scenarios (a box is selected randomly, a lightbulb picked is defective, and two lightbulbs chosen are wrong). Let's use the following symbols: B1 (Box 1), B2 (Box 2), D (faulty lightbulb).
(a) The probability of a lightbulb being defective, given it came from Box 1 (P(D|B1)), is 0.10. The total likelihood of a lightbulb being inferior (P(D)) can be worked out from the total of defective lightbulbs divided by the total number of lightbulbs. The probability we're after, according to Bayes' theorem, is P(B1|D) = [P(D|B1)*P(B1)] / P(D).
(b) This question is more complex but can be solved similarly. Assuming the lightbulbs are selected independently, the probability of picking two defective lights from a given box is simply the square of picking one defective lightbulb from that box. Thus, we calculate P(2D|B1) = [P(D|B1)]^2 = (0.10)^2 = 0.01 (or 1%). Then, we use Bayes' theorem in part (a) to find P(B1|2D).
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Emma's total bill for dinner was $20. The cost of her dessert was 30% of the total bill. What was the cost of her dessert?
Answer:
The answer is $6
Step-by-step explanation:
20 divided by 30% is 6! So it’s therefore 6$
Let f(x)=x2+17x+72 .
What are the zeros of the function?
Enter your answers in the boxes.
Hence zeros of function are
,x=-9, x=-8
Value of x that makes function value 0.
How to solve?[tex]x^{2[/tex] +17x+72=0
[tex]x^{2}[/tex]+ 8x+9x+72=0
x(x+8)+9(x+8)=0
(x+9)(x+8)=0
x=-9,-8
Hence ,x=-9, x=-8
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Final answer:
The zeros of the function f(x) = x² + 17x + 72 are -9 and -8, found by factoring the quadratic equation.
Explanation:
To find the zeros of the function f(x) = x² + 17x + 72, we need to solve the equation for x when f(x) = 0. This can be done by factoring the quadratic equation if possible.
The quadratic factors as (x + 9)(x + 8) = 0. So the solutions to the equation x² + 17x + 72 = 0 are:
x = -9
x = -8
Therefore, the zeros of the function are -9 and -8.
Two particle with charges q and −q are fixed at the vertices of an equilateral triangle with sides of length
a. if k = 1/4π 0, the work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles is:
Answer:
k(qq)/r^2 times the length of the distnace
Step-by-step explanation:
Force times distance. The Electrical force is the only thing you have to find first.
The work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles is -kq^2/a.
Explanation:To find the work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles, we need to calculate the electrostatic potential energy. The potential energy is given by the equation:
U = kqQ/r
where U is the potential energy, k is the electrostatic constant, q and Q are the charges, and r is the distance between the charges.
In this case, we have two charges of magnitude q and -q at the vertices of an equilateral triangle. The distance from the center of the triangle to each charge is a/2, where a is the length of the side of the triangle. Therefore, the potential energy is:
U = (1/4πε0)q(-q)/a
where ε0 is the permittivity of free space. Simplifying the expression, we get:
U = -kq2/a
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look at the picture for the question
Please answer
Answer:
[tex]\large\boxed{D.\ 12x^2-29x+14}[/tex]
Step-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex](3x-2)(4x-7)=(3x)(4x)+(3x)(-7)+(-2)(4x)+(-2)(-7)\\\\=12x^2-21x-8x+14\qquad\qquad\text{combine like terms}\\\\=12x^2+(-21x-8x)+14=12x^2-29x+14[/tex]
What basic trigonometric identity would you use to verify that cot x sin x =cos x
[tex] \cot(x) \sin(x) = \frac{ \cos(x) }{ \sin(x) } \sin(x) = \cos(x) \\ \Rightarrow b. \cot(x) = \frac{ \cos(x) }{ \sin(x) } [/tex]
Answer:
B
Step-by-step explanation:
Help with this question, please!! I need serious help on this question!
Answer:
[tex]\large\boxed{d_2=15\ cm}[/tex]
Step-by-step explanation:
The formula of an area of a kite:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
d₁, d₂ - diagonals
We have A = 120 cm² and d₁ = 16 cm. Substitute:
[tex]\dfrac{16d_2}{2}=120[/tex]
[tex]8d_2=120[/tex] divide both sides by 8
[tex]d_2=15\ cm[/tex]
PLEASE HELP! WILL MARK THE BRAINLIEST ANSWER!
x ÷ 5 = 1/10
X=1/2
Explanation
Multiple both sides times 5
Then the 5 just cancels out on the left side and you’re left with 1/2
There are 10 rolls of film in a box and 3 are defective. two rolls are to be selected, one after the other. what is the probability of selecting a defective roll followed by another defective roll?
Answer:
1 / 15 = 0.06666666666....Step-by-step explanation:
Total Number of Rolls = 10
Number of Defective Rolls = 3
Probability = Number of Defective Rolls / Total Number of Rolls
Probability = 3 / 10
Now there is one less defective roll.
Total Number of Rolls = 10 - 1
Number of Defective Rolls = 3 - 1
Total Number of Rolls = 9
Number of Defective Rolls = 2
Probability = Number of Defective Rolls / Total Number of Rolls
Probability = 2 / 9
Multiply the two probabilities together to find the overall probability.
3 / 10 * 2 / 9
3 * 2 = 6
10 * 9 = 90
6 / 90
Simplify
6 / 90 = 3 / 45 = 1 / 15 = 0.06666666666....
To find the probability of selecting two defective rolls of film in a row from a box of 10 rolls where 3 are defective, you multiply the probability of each selection. The result is a 1/15 chance of selecting two defective rolls consecutively.
Explanation:The question deals with the concept of probability without replacement. In this scenario, we calculate the probability by considering each step independently. Initially, there are 10 rolls of film, and 3 are defective. The probability of selecting a defective roll first is 3 out of 10, or 3/10. Once a defective roll has been selected, there are now 9 rolls left with 2 being defective. The probability of selecting another defective roll is then 2 out of 9, or 2/9. To find the overall probability of both events happening in sequence ('and' probability), we multiply the probabilities of each step:
P(First defective and second defective) = P(First defective) * P(Second defective | First defective) = (3/10) * (2/9) = 6/90 = 1/15.
Therefore, the probability of selecting two defective rolls in a row is 1/15.
The temperature at a point (x, y, z) is given by t(x, y, z) = 200e−x2 − 3y2 − 7z2 where t is measured in °c and x, y, z in meters. (a) find the rate of change of temperature at the point p(4, −1, 4) in the direction towards the point (5, −5, 6).
Looks like the temperature is given by
[tex]t(x,y,z)=200e^{-x^2-3y^2-7z^2}[/tex]
We have gradient at any point [tex](x,y,z)[/tex]
[tex]\nabla t(x,y,z)=200e^{-x^2-3y^2-7z^2}(-2x,-6y,-14z)[/tex]
Then the rate of change of [tex]t[/tex] at [tex]p[/tex] in the direction of (5, -5, 6) is given by
[tex]\nabla t(4,-1,4)\cdot\dfrac{(5,-5,6)}{\|(5,-5,6)\|}=\left(-\dfrac{400}{e^{131}}(4,-3,28)\right)\cdot\dfrac{(5,-5,6)}{\sqrt{86}}=-\dfrac{40600}{e^{131}}\sqrt{\dfrac2{43}}[/tex]
which is very nearly 0.
The rate of change of temperature at the point p(4, -1, 4) in the direction towards the point (5, -5, 6) can be found by computing the gradient vector at p, obtaining a unit direction vector towards the other point, and calculating their dot product.
Explanation:To find the rate of change in the direction towards the point (5, -5, 6), we need to compute the gradient vector of the temperature at point p(4, -1, 4), and then calculate the directional derivative in the direction towards the other point.
First, we calculate the partial derivative of t with respect to x, y, and z. These derivatives give us the gradient vector ∇t at point p. The gradient vector represents the direction of the steepest incline at p and its magnitude gives the rate of increase of t.
Next, we need to find the unit vector in the direction towards point (5,-5,6) from p. Subtracting the coordinates of p from the other point gives us the direction vector. Normalizing this vector gives us the unit direction vector.
Finally, the rate of change of temperature at p in the direction towards the other point is given by the dot product of ∇t at p and the unit direction vector. This is known as the directional derivative of t at p in the mentioned direction.
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Chris Nazarro had total travel expenses of $872. His transportation cost was $136. The hotel cost was $210 and business materials cost $500. If his lunch cost 30% of his dinner, how much was dinner to the nearest cent?
Answer:
[tex]\$20[/tex]
Step-by-step explanation:
Let
x-----> the cost of his lunch
y----> the cost of his dinner
we know that
[tex]x+y=872-136-210-500[/tex]
[tex]x+y=26[/tex] -----> equation A
[tex]x=0.3y[/tex] ---> equation B
substitute equation B in equation A
[tex]0.3y+y=26[/tex]
[tex]1.3y=26[/tex]
[tex]y=\$20[/tex] -----> the cost of the dinner
How do you know if a system or equations has one solution, no solution, or infinitely many solutions
Step-by-step explanation:
We transform the system of equations to the form:
[tex]\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right[/tex]
Where a & b and d & e are relatively prime number.
1.If a ≠ d or b ≠ e then the system of equations has one solution.
Example:
[tex]\left\{\begin{array}{ccc}2x-3y=-4\\3x+3y=9\end{array}\right[/tex]
Add both sides of equations:
[tex]5x=5[/tex] divide both sides by 5
[tex]x=1[/tex]
Substitute it to the second equation:
[tex]3(1)+3y=9[/tex]
[tex]3+3y=9[/tex] subtract 3 from both sides
[tex]3y=6[/tex] divide both sides by 3
[tex]y=2[/tex]
[tex]\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]
2.If a = d and b = e and c = f then the system of equations has infinitely many solutions.
Example:
[tex]\left\{\begin{array}{ccc}2x+3y=5\\2x+3y=5\end{array}\right[/tex]
Change the signs in the second equation. Next add both sides of equations:
[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=5\\-2x-3y=-5\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}[/tex]
[tex]\boxed{x\in\mathbb{R},\ y=\dfrac{5-2x}{3}}[/tex]
3.If a = d and b = e and c ≠ f then the system of equations has no solution.
Example:
[tex]\left\{\begin{array}{ccc}3x+2y=6\\3x+2y=1\end{array}\right[/tex]
Change the signs in the second equation. Next add both sides of equations:
[tex]\underline{+\left\{\begin{array}{ccc}3x+2y=6\\-3x-2y=-1\end{array}\right}\\.\qquad0=5\qquad\bold{FALSE}[/tex]
The height of a pyramid is 15 inches. The pyramid's base is a square with a side of 5 inches. What is the pyramid's volume?
Answer:
The pyramid's volume is [tex]125\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=(1/3)Bh[/tex]
where
B is the area of base of pyramid
h is the height of the pyramid
Find the area of the base B
[tex]B=5^{2}=25\ in^{2}[/tex] -----> is a square
[tex]h=15\ in[/tex]
substitute the values
[tex]V=(1/3)(25)(15)=125\ in^{3}[/tex]
A store marks up merchandise 40% for profit. If an item costs the store $15, what is the selling price?
Answer:
The selling price is $21
Step-by-step explanation:
What is the markup
Take the original price and multiply by the markup percent
markup = 15*40%
= 15*.4
= 6
The new price is the original price plus the markup
new price = 15+6
new price = 21
The selling price is $21
What is the largest whole number that will round up or down to 500 if we're rounding to the nearest hundred?
Answer:
549
Step-by-step explanation:
The next larger whole number, 550, will round up to 600.
The largest whole number that rounds to 500 is 549 when rounding to hundreds.
Solve for x in the given interval.
sec θ = -4.0545, for 0≤θ≤2π
Answer:
The answer is Ф = 1.82 or 4.46 ⇒ answer (c)
Step-by-step explanation:
* The domain of the function is 0 ≤ Ф ≤ 2π
- Lets revise the ASTC rule to solve the problem
# In the 1st quadrant all trigonometry functions are +ve
# In the 2nd quadrant sinФ and cscФ only are +ve
# In the 3nd quadrant tanФ and cotФ only are +ve
# In the 4th quadrant cosФ and secФ only are +ve
* Lets solve the problem
∵ secФ = -4.0545 ⇒ negative value
∴ Angle Ф is in the 2nd or 3rd quadrant
- In the 2nd quadrant Ф = π - α ⇒ (1)
- In the 3rd quadrant Ф = π + α ⇒ (2)
where α is an acute angle
* Now use the calculator to find α with radiant mode
- Let secα = 4.0545
∴ cosα = 1/4.0545
∴ α = cos^-1(1/4.0545) = 1.321585
* Substitute the value of α in (1) and (2)
∴ Ф = π - 1.321585 = 1.82
∴ Ф = π + 1.321585 = 4.46
* The answer is Ф = 1.82 or 4.46
For the normal distribution, the mean plus and minus 1.96 standard deviations will include about what percent of the observations
Answer:
95%.
Step-by-step explanation:
That would be about 95% of the observations.
The percentage within 1 standard deviation is about 68%.
What is the domain of f(x) =3 square x?
Answer:
Set of all real numbers
Step-by-step explanation:
Given in the question the equation:
f(x) = ∛(x)
The domain of a cube root function is the set of all real numbers.
The interval notation (-∞ , ∞)
Cube Root of negative numbers exists:
Negative numbers can't have real number square roots, but negative numbers can have real number cube roots because when you are multiplying an odd number of negative numbers, the result is negative.
Example
(-2)³ = (-2)(-2)(-2) = -8
. Find the indicated dot product. r = <9, -7, -8>, v = <3, 4, 7>, w = <6, -9, 7> v ? w (1 point) <-27, 28, 56> <18, -36, 49> 18 31
The dot product is a scalar product, so you can eliminate the first two choices right away.
We have
[tex]v\cdot w=\langle3,4,7\rangle\cdot\langle6,-9,7\rangle=3\cdot6+4\cdot(-9)+7\cdot7=31[/tex]
Answer:
31
Step-by-step explanation:
v ⋅ w = (3)(6) + (4)(-9) + (7)(7)
v ⋅ w = 18 - 36 + 49
v ⋅ w = 31
The radius of a sphere is 6 units. Which expression represents the volume of the sphere in cubic units.
[tex] \frac{3}{4} \pi(6) {}^{2} \\ \\ \frac{4}{3} \pi(6) {}^{3} \\ \\ \frac{3}{4} \pi(12) {}^{2} \\ \\ \frac{4}{3} \pi(12) {}^{3} [/tex]
60 points Need help Asap
Answer:
45 units ^2
Step-by-step explanation:
make sure to divide the triangle and sqaure up when finding the area of this polygon..
hope this helps!!
Phil is 23 years older than Keith. In two years Phil will be twice as old as Keith will be. How old is Keith in years?
Answer:
44 years old
Step-by-step explanation:
The deifference between their ages is always the same. So 23x2=46
but that is in 2 years so we -2 from 46 =44
Answer:
44
Step-by-step explanation:
can anyone solve this problem
Answer:
the answer is D according to what i got
~batmans wife
Answer:
E. b/3 + 3
Step-by-step explanation:
For all real number b and c, if the product of c and 3 is b,
mathematically; 3c = b...(1)
To find the sum of c and 3 in terms of b;
Mathematically, the sum of c and 3 gives c+3...(2)
From equation 1, c = b/3
Substituting c = b/3 into equation 2, we will have;
(b/3) + 3 option E
= (b+9)/3
Triangle T was dilated to form triangle T'. Which ratio is the correct scale factor?
Please answer fast and correctly
Answer:
5/9
Step-by-step explanation:
The scale factor by which T was dilated is ...
(side of T')/(corresponding side of T)
= 20/36 = 10/18 = 5/9 . . . (reduced form)
Answer:
C) the answer is 5/9 or C
Step-by-step explanation:
i got it roght on the edgen quiz.
a mailing container for posters is made from 87.4 square inches of cardboard the container is in the shape of a triangular prism the base of the prism is an equilateral triangle with 2- inch side lengths and a height of 1.7 inches what is the length of the container
Answer:
The length of the container is [tex]14\ in[/tex]
Step-by-step explanation:
we know that
The surface area of a triangular prism (a mailing container) is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
L is the length of the container
step 1
Find the area of the base B
[tex]B=\frac{1}{2}(2)(1.7)=1.7\ in^{2}[/tex]
step 2
Find the perimeter of the base P
[tex]P=3(2)=6\ in[/tex]
step 3
Find the length L of the container
we have
[tex]SA=87.4\ in^{2}[/tex]
[tex]B=1.7\ in^{2}[/tex]
[tex]P=6\ in[/tex]
substitute and solve for L
[tex]87.4=2(1.7)+(6)L[/tex]
[tex]L=[87.4-2(1.7)]/(6)[/tex]
[tex]L=14\ in[/tex]
Find the missing measurement. Round your answer to the nearest tenth.
Answer:
[tex]7.30\ mi[/tex]
Step-by-step explanation:
Let
b-----> the base of the missing measurement of the parallelogram
we know that
The area of the parallelogram is equal to
[tex]A=bh[/tex]
we have
[tex]A=27\ mi^{2}[/tex]
so
[tex]27=bh[/tex] ------> equation A
In this problem
[tex]h=3.7\ mi[/tex]
substitute the value in the equation A and solve for b
[tex]27=b(3.7)[/tex]
[tex]b=27/3.7=7.30\ mi[/tex]
What is the total surface area of this square pyramid?
Answer:
The total surface area of this square pyramid is [tex]297\ mm^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of a square pyramid is equal to
[tex]SA=b^{2} +4[\frac{1}{2}(b)(h)][/tex]
we have
[tex]b=9\ mm[/tex] ----> the length side of the square base
[tex]h=12\ mm[/tex] ----> the height of the triangular faces
substitute the values
[tex]SA=9^{2} +4[\frac{1}{2}(9)(12)]=297\ mm^{2}[/tex]
A sheet of postage stamps 3 stamps wide by 4 stamps long covers 9 square inches. Given the same size stamps, how many square inches would be covered by a sheet 6 stamps by 10 stamps?
Answer: 45 in²
Step-by-step explanation:
3 stamps by 4 stamps = 12 stamps
9 in / 12 stamps = 0.75 in/stamp
6 stamps by 10 stamps = 60 stamps
60 stamps * 0.75 in/stamp = 45 in²
Solve x^2-8x=20 by completing the square. Which is the solution set of the equation?
Step-by-step explanation:
x^2 - 8x = 20
1. Subtract 20 from both sides
x^2 - 8x - 20 = 20 - 20
2. Simplify
x^2 - 8x - 20 = 0
3. Factor the equation out by grouping
(x - 10)(x + 2) = 0
4. Change signs:
x = 10, x = -2
Hope This Helped!!
~Shane
Answer:{-2,10}
Step-by-step explanation:
trust
oop please help quick!!