a) The probability that during next second the number of alpha particales omitted from 1 gram is at most 6 is 0.998.
b) The probability that during next second the number of alpha particales omitted from 1 gram is at least 2 is 0.985.
c) The probability that during next second the number of alpha particales omitted from 1 gram is at least 3 and at most 6 is 0.679.
This problem is an application of the Poisson distribution, which is commonly used to model the number of events occurring in a fixed interval of time. In this case, we are interested in the number of alpha particles emitted by 1 gram of the radioactive element in one second.
The average rate of emission is given as 3.9 alpha particles per second. This means that the mean or expected number of alpha particles emitted by 1 gram of the element in one second is also 3.9.
(a) To find the probability that at most 6 alpha particles are emitted from 1 gram of the element in one second, we can use the Poisson distribution with λ=3.9 and x=0, 1, 2, 3, 4, 5, or 6.
The probability is given by the cumulative distribution function (CDF) of the Poisson distribution, which can be calculated using software or a table. For example, using a Poisson table or calculator, the probability is approximately 0.998.
(b) To find the probability that at least 2 alpha particles are emitted, we can use the complementary probability: P(at least 2) = 1 - P(none or 1). Using the Poisson distribution with λ=3.9 and x=0 or 1, we find P(none or 1) = 0.015. Therefore, P(at least 2) = 1 - 0.015 = 0.985.
(c) To find the probability that at least 3 and at most 6 alpha particles are emitted, we need to add the probabilities for x=3, 4, 5, and 6. Using the Poisson distribution with λ=3.9, we can calculate P(x=3) = 0.089, P(x=4) = 0.172, P(x=5) = 0.212, and P(x=6) = 0.206. Therefore, the probability is approximately 0.679.
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the number 5/3 can be best described as a(n) ___.
Answer: Proper fraction
Step-by-step explanation:
A proper fraction is a fraction that has its numerator value less than the denominator.
For example, ⅔, 6/7, 8/9, etc. are proper fractions.
This is parallelograms practice and I don’t get it at all!! Please help me guys
Step-by-step explanation:
p-grams have equal opposite side lengths
soooo
5x+7 = 27
x = 4
then 22x = 22(4) = 88 units ( this is also AB length)
What is the value of
∠FDE given the following image?
The value of ∠FDE is 36°
Define the term angles?An angle is a geometric figure formed by two rays, or lines that extend infinitely in opposite directions, that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays.
Here given a right angle ∠CDE = 90°
So, we can say that,
∠CDF + ∠FDE = ∠CDE
(2x)° + (x+9)° = 90°
(3x + 9)° = 90°
Simplify it, x = 27°
So, the value of ∠FDE = (x+9)° = (27+9)° = 36°
Therefore, the value of ∠FDE is 36°
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The angle FDE is 36°. The required answer for the given question is option (A). 36°.
What is the value of <FDE?Trigonometry angles are the angles provided by the trigonometric function ratios. Trigonometry is the study of the connection between angles and triangle sides. Angle values vary from 0 to 360 degrees.
An angle is a shape in geometry made by two rays or lines that stretch indefinitely in opposite directions and have a common endpoint known as the vertex. The quantity of rotation among the two rays determines the size of an angle.
From the given figure,
∠CDF + ∠FDE = 90
Thus,
(2x)+(x+9) = 90
3x + 9 = 90
3x = 81
x = 27
Then we will have that the angle FDE is:
∠FDE = (27) + 9
∠FDE = 36
The angle of FDE is 36°
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how can the union and intersection of n sets that all are subsets of the universal set u be found using bit strings?
The union and intersection of n sets that are all subsets of the universal set u can be found using bit strings.
Bit strings are a way of representing sets as strings of binary digits. To represent a set, each element is assigned a digit of 0 or 1. A 1 indicates that the element is in the set, while a 0 indicates that the element is not in the set.
The union of the sets is found by combining the bit strings and setting any digit that is 1 in any of the sets to a 1. The intersection is found by comparing the bit strings and setting any digit that is 1 in all of the sets to a 1.
By using bit strings, we can quickly and accurately find the union and intersection of n sets that are all subsets of the universal set u.
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I NEED HELP ON THIS ASAP!
Answer:
16 represents the hours available to sew gloves.
2 represents the cost of producing gloves for a small pair.
Step-by-step explanation:
Please helpppppp! I really don't understand
Answer:
AB=8.1 and B=29.6
Step-by-step explanation:
1) To find the measure of AB, use the law of cosines
[tex]c^2=4^2+7^2-2(4)(7)cos(90)[/tex]
[tex]c^2 = 16+49 -56cos(90)\\c^2= 65\\c=8.1[/tex]
2) Use law of sines to find the measure of B
[tex]\frac{8.1}{sin(90)} =\frac{4}{sin(B)}[/tex]
B=29.6
Which statement describes the graph of this polynomial function?
f (x) = x Superscript 5 Baseline minus 6 x Superscript 4 Baseline + 9 x cubed
Answer:
The statement that describes the graph of the polynomial function f (x) = x^5 - 6x^4 + 9x^3 is that it has a local maximum at x = 0 and a local minimum at x = 2. The degree of the polynomial is 5, which means it has five zeros or x-intercepts. The leading coefficient is positive, which indicates that the graph will rise to the left and right. The function has a point of inflection at x = 1.5, where the concavity changes from up to down. Overall, the graph of this polynomial function has a typical "upside-down U" shape with local extrema and a point of inflection.
Grace plans on going to the amusement park this Friday. It costs $10.00 to enter the park, and then $2.50 for every ride that Grace goes on. What will be the total cost if Grace goes on 7 rides?
Answer: 27.50
Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50
Identify the two choices that best completes the statement below.
What is the sum of the first 10 terms of the series 1 + 2 + 4 + 8...?
The sum of the first 10 terms of the geometric progression that is given in the question is 1023.
What is geometric progression ?
Geometric progression, also known as geometric sequence, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed constant. This fixed constant is called the common ratio.
The given series is a geometric progression, where each term is obtained by multiplying the preceding term by 2. The first term is 1, and the common ratio is 2.
The sum of the first n terms of a geometric progression is given by the formula:
[tex]S_n = a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Using this formula, we can find the sum of the first 10 terms of the given series as:
[tex]S_{10} = 1(1 - 2^{10}) / (1 - 2)[/tex]
[tex]= 1(1 - 1024) / (-1)[/tex]
[tex]= 1023[/tex]
Therefore, the sum of the first 10 terms of the series 1 + 2 + 4 + 8... is 1023.
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volume of a sphere = ³, where r is the radius. The radius of a spherical planet is 6052 km, and its mass is 4.87 × 1027g. Calculate the density of the planet in kilograms per cubic metre (kg/m³). Give your answer in standard form to 3 s.f.
Answer:
5240 kg/m³
Step-by-step explanation:
You want the average density of a planet with radius 6052 km and mass 4.87×10^27 g.
Unit conversionThe mass is given in grams, and the corresponding unit in the desired answer is kilograms. There are 1000 g in 1 kg, so 4.87×10^27 g = 4.87×10^24 kg.
The radius is given in km, and the corresponding unit in the desired answer is meters. There are 1000 meters in 1 km, so 6052 km = 6052×10^3 m. (We could adjust the decimal point, but we choose to let the calculator do that.)
DensityThe units of density tell you it is computed by dividing the mass by the volume:
ρ = mass/volume
The volume of the sphere is found using the given formula, so the density is ...
ρ = (4.87×10^24 kg)/(4/3π(6052×10^3 m)^3)
ρ ≈ 5240 kg/m³
The average density of the planet is about 5240 kg/m³.
__
Additional comment
This is comparable to the average density of Earth, which is about 5520 kg/m³.
1. Divide and simplify. **Please show all work to receive full credit 1/x+4 ÷ x-3/ x²+7x+12
After dividing and simplifying we get (x-3)/(x+3)
What is division?One of the four fundamental operations of arithmetic, or how numbers are combined to create new numbers, is division. The additional operations are addition, subtraction, and multiplication.
At a fundamental level, counting the instances in which one number is contained within another is one interpretation of the division of two natural numbers. There is no requirement that this quantity be an integer. For instance, if there are 20 apples and they are divided equally among four people, each person will get 5 apples (see picture).
The integer quotient, which is the quantity of times the second number is entirely contained in the first number, and the remainder are both produced by the division with remainder or Euclidean division of two natural numbers.
1/(x+4) divide by [tex](x-3)/(x^2 + 7x +12)[/tex]
Simplify : [tex]x^2 +7x +12[/tex]
[tex]x^2 + (3+4)x + 12[/tex]
[tex]x^2 + 3x +4x + 12[/tex]
[tex]x(x + 3) + 4(x + 3)[/tex]
[tex](x+3)(x+4)[/tex]
[tex]1/(x + 4) x (x-3)/(x+3)(x-4)[/tex]
After dividing and simplifying we get the following answer;
[tex]= (x-3)/(x+3)[/tex]
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analysis of a pert problem shows the estimated time for the critical path to be 108 days with a variance of 64. there is a .90 probability that the project will be completed before approximately day: group of answer choices 108. 98. 115. 118. 109.
There is a .90 probability that the project will be completed before approximately day 118.
The given information can be solved by using the formula of z-score as follows:
Z = (X - μ)/σ
Where: Z = z-score
X = the time for project completion
μ = the mean time for the critical path
σ = standard deviation for the critical path
σ² = variance of the critical pathσ = √64
σ = 8
Given that the mean time for the critical path is μ = 108 days and σ = 8 days,
Therefore, the z-score of the completion of the project before 108 days is given by:
Z = (X - μ)/σ0.90
= P(Z < z)
= P(Z < (X - 108)/8)P(Z < (X - 108)/8)
= 0.90
Using a z-table or calculator, we find the z-value to be 1.28.
Then,1.28 = (X - 108)/8
Multiplying both sides by 8, we get:10.24 = X - 108
Adding 108 to both sides, we get: X = 118.24
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a state's license plates consist of 4 letters followed by 5 digits. how many possible license plates can be issued using this condition?
In the following question, among the conditions given, There are 26^4 x 10^5 possible license plates that can be issued using this condition.
Hence, This is because the license plates consist of 4 letters and 5 digits. There are 26 possible letters that can be used in the first four places, so the total possible combinations of 4 letters is 26^4. There are 10 possible digits that can be used in the last five places, so the total possible combinations of 5 digits is 10^5. Multiplying these two together gives the total number of possible license plates: 26^4 x 10^5.
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There are a total of $26^4 × 10^5$ possibilities, which simplifies to 26,000,000,000 (twenty-six billion) possibilities. Therefore, with this condition, twenty-six billion license plates can be issued.
A state's license plates consist of 4 letters followed by 5 digits.
How many possible license plates can be issued using this condition?
When designing a license plate, the condition provided in the question suggests that a license plate should consist of 4 letters followed by 5 digits.
Therefore, we can count the total number of license plates in two phases.
The number of choices for each segment must be taken into account separately for the letters and the numbers.
When considering the letter possibilities, there are 26 options for each position since there are 26 letters in the alphabet.
For the first 4 positions, there are a total of $26^4$ = 456,976 possibilities.
Similarly, for the last 5 positions,
there are 10 options for each position since there are 10 digits.
There are $10^5$ = 100,000 possibilities for the last 5 positions.
The entire plate's total number of combinations is obtained by multiplying these numbers.
There are a total of $26^4 × 10^5$ possibilities
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the sum of the proportions for all categories of a variable will be select one: a. 100.00 b. 10.00 c. 1.00 d. 0.10
In the following question, among the given options, The sum of the proportions for all categories of a variable will be (C.) "1.00."
What is proportion? Proportions are usually represented as a decimal numbers between 0 and 1. They can also be represented as a percentage between 0 and 100. Proportions show the relationship between a particular number and a whole group. The total sum of proportions will always be equal to 1.00, which represents the entire group or population. So the answer to the given question is c. 1.00.
ExplanationThe sum of the proportions for all categories of a variable will be 1.00 because of the following: Proportions of a categorical variable are used to analyze data in statistics. A proportion is a fraction of a whole group that represents a part of that group. Proportions are usually represented as a decimal numbers between 0 and 1. They can also be represented as a percentage between 0 and 100. The sum of the proportions for all categories of a variable will be 1.00 representing the whole group or population, which is equal to 100%. This is the same as saying that the proportions for all categories of a variable should add up to 100%.
Therefore, the correct answer to the question is c. 1.00.
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please help 20 points 10 ft 20 ft 15 ft Find the area. A = [?] ft² Round to the nearest hundredth. Remember: A = πr² Use 3.14 for π. Enter
Answer:
about 307.08 square feet
Step-by-step explanation:
[tex] \frac{1}{2} (20)(15) + \frac{1}{2} \pi( {10}^{2} ) = 307.08[/tex]
If the function, g(x), has the ordered pairs (-4, 15), (-2, 3), and (0, -1), fill in the ordered pairs that know exist on the graph of g−1(x)
Answer:
(15, - 4 ) , (3, - 2 ) , (- 1, 0 )
Step-by-step explanation:
given a point (x, y ) on a function f(x) , then the corresponding point on the inverse function is (y, x )
given the points on g(x) , then the corresponding points on [tex]g^{-1}[/tex] (x) are
(- 4, 15 ) → (15, - 4 )
(- 2, 3 ) → (3, - 2 )
(0, - 1 ) → (- 1, 0 )
a bag is filled with 200 silver coins and 123 gold coins. what is the theoretical probability of not pulling out a silver coin?
The theoretical probability of not picking the silver coin will be 0.38 .
Given,
200 silver coins and 123 gold coins are filled in a bag .
Now,
Total number of coins in a bag = gold + silver coins
Total number of coins in a bag = 200 + 123
Total number of coins in a bag = 323
Further ,
Probability of taking silver coin = 200/323
Probability of taking silver coin = 0.619.
probability of taking gold coin = 123/323
probability of taking gold coin = 0.38
Hence the probability of not selecting silver coin is 0.38 .
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which set of numbers can make the inequality below true? 26> n + 15
Answer:
[tex]26 > n + 15[/tex]
[tex]11 > n[/tex]
[tex]n < 11[/tex]
pls help math scientific notation (view photo)
Just ignore this answer, its incorrect
*edited*
Factor 64v+8w. ASAPPP PLSS
Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran
Step-by-step explanation:
evaluate the double integral. 8y2 da, d is the triangular region with vertices (0, 1), (1, 2), (4, 1) d
The value of the double integral is 128/27 - 32/9 + 8ln2/3. From triangular region with vertices (0, 1), (1, 2), (4, 1) d.
To evaluate the double integral, we first need to set up the limits of integration. Since the region D is a triangle, we can use the following limits:
0 ≤ x ≤ 1
1 + x ≤ y ≤ 4 - x
The integral then becomes:
∫0^1 ∫1+x^4-x 8y^2 dy dx
Evaluating the integral with respect to y first, we get:
∫0^1 ∫1+x^4-x 8y^2 dy dx = ∫0^1 [(8/3)(y^3)]1+x^4-x dx
= ∫0^1 [(8/3)(1+x^3)^3 - (8/3)(1+x^2)^3] dx
= 128/27 - 32/9 + 8ln2/3
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answers on a multiple choice test have choices a, b, c, d. the instructor has chosen answers randomly according to a discrete uniform distribution. what is the probability the first 3 questions have the same answer choice?
The probability that the first three questions have the same answer choice is 1/4, since there are four answer choices and the instructor is randomly selecting the answers according to a discrete uniform distribution. This means that each answer choice has an equal probability of being chosen. Therefore, the probability of all three questions having the same answer is 1/4.
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The yard pictured below has algebraic expressions for its side lengths, in metres.
Find a simplified algebraic expression for the perimeter of the yard.
Use your expression to find the perimeter in meters, if the value of x=3 m . Show your steps.
The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.
The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.
In the given figure, the yard is in the shape of a rectangle with dimensions (4x - 6) m and (2x + 3) m. The perimeter of a rectangle is the sum of the lengths of all four sides, which can be expressed as:
Perimeter = 2(Length + Width)
Perimeter = 2(4x - 6 + 2x + 3) m
Perimeter = 2(6x - 3) m
Perimeter = 12x - 6 m
So, a simplified algebraic expression for the perimeter of the yard is 12x - 6 m.
To find the perimeter in meters when x = 3 m, substitute x = 3 into the algebraic expression for perimeter:
Perimeter = 12(3) - 6 m
Perimeter = 30 m
Therefore, the perimeter of the yard when x = 3 m is 30 meters.
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suppose 60% of american adults believe martha stewart is guilty of obstruction of justice and fraud related to insider trading. we will take a random sample of 20 american adults and ask them the question. then the sampling distribution of the sample proportion of people who answer yes to the question is: group of answer choices
Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading.
We will take a random sample of 20 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is a binomial distribution.
What is a binomial distribution?A binomial distribution is a statistical distribution that represents the likelihood of one of two outcomes in a sequence of independent trials. Binomial distributions can be used to model a variety of phenomena, including flipping coins, rolling dice, and performing multiple independent experiments.
The probability of getting k successes in n trials in a binomial distribution with probability of success p and probability of failure q is given by the following formula:P (k) = nCk * p^k * q^(n-k)Where nCk is the binomial coefficient, which represents the number of ways to select k items from a set of n items without regard to order.
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Is 8 a reasonable solution to log(-x)=log(x-16)?
A) Yes, 8 is a reasonable solution because 8 is positive and -(8)=(8)-16
B) No, 8 is NOT a reasonable solution because at x=8, the logarithm is not defined.
Find the distance between the points (9,7) and (6,3).
Let (x1, y1) = (9,7) and (x2, y2) = (6,3)
By distance formula,
d = (x2 - x1)² + (y2 - y1)²
d = (6 - 9)² + (3 - 7)²
d = (-3)² + (-4)²
d = 9 + 16
d = 25 units
there are 75 people at the city swim park today. everyone in the park was wearing swim suits or sunglasses, some people had both. how many people had swim suits on but not sunglasses, if you know 63 people have swim suits on and 43 have sunglasses?
If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.
To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.
We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:
total = swim suits + sunglasses - both
Substituting in the given values, we get:
75 = 63 + 43 - x
Simplifying, we get:
x = 31
Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:
63 - 31 = 32
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The table shows the dimensions of two fenced-in areas at the dog park. How many times greater is the area enclosed by the wood fence than the area enclosed by the metal fence
The area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence. So the correct answer is d. 7 3/4.
What is area?When measuring the area of a shape, we are determining the amount of surface the shape takes up.
To calculate the area enclosed by each fence, we must multiply the length and width of each.
The area enclosed by the wood fence is
6 1/2 x 2 1/4 = 14 7/8 square yards,
and the area enclosed by the metal fence is
2 3/4 x 2 1/2 = 6 7/8 square yards.
To determine how many times greater the area enclosed by the wood fence is than the area enclosed by the metal fence, we must divide the area of the wood fence by the area of the metal fence:
14 7/8 / 6 7/8 = 7 3/4.
This means the area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence.
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i need the answers in about 10 mins
a normal distribution has a mean of 61 and a standard deviation of 14. what is the median? (enter an exact number as an integer, fraction, or decimal.)
The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.
This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.
Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.
It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.
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