The simple random sample of 200 eggs
Statistic=Proportion of eggs in the sample that contain salmonella.
p = 0.045
The population is the individuals that are being studied.
population=All eggs in one day
A sample is the part of the population of which information was actually collected.
Sample=The simple random sample of 200 eggs
A parameter is a descriptive measure for a population.
Parameter=Proportion of eggs shipped that day that contain salmonella.
p = 0.1 % =0.001
A statistic is a descriptive measure for a sample.
STATISTIC=Proportion of eggs in the sample that contain salmonella.
p=9÷200 = 0.045
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About 13% of the students at high school have a part time job what is the probability that they’re will be between 33 and 45 with part time jobs in a randomly selected group of 300
A:.173
B.736
C.694
D.172
The probability that they’re will be between 33 and 45 with part time jobs in a randomly selected group of 300 is given as follows:
B. 0.736.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in this problem are given as follows:
p = 0.13, n = 300.
Hence the mean and the standard deviation are given as follows:
[tex]\mu = 300 \times 0.13 = 39[/tex][tex]\sigma = \sqrt{300 \times 0.13 \times 0.87} = 5.82[/tex]Using continuity correction, the probability of X between 33 and 45 is (32.5 < X < 45.5), which is the p-value of Z when X = 45.5 subtracted by the p-value of Z when X = 32.5, hence:
X = 45.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (45.5 - 39)/5.82
Z = 1.12
Z = 1.12 has a p-value of 0.8686.
X = 32.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (32.5 - 39)/5.82
Z = -1.12
Z = -1.12 has a p-value of 0.1314
Hence:
0.8686 - 0.1314 = 0.736 (approximately).
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please just say the answer
The angles ∠1 and ∠2 are vertical angles. Vertical angles are congruent and according to the definition of congruency, ∠1 = ∠2.
The completed table used to prove that ∠1 ≅ ∠2 is presented as follows;
Statement [tex]{}[/tex] Reasons
1. m∠1 + m∠3 = 180° [tex]{}[/tex] 1. Linear pair angles are supplementary
m∠2 + m∠3 = 180°
2. m∠1 + m∠3 = m∠2 + m∠3 [tex]{}[/tex] 2. Substitution
3. m∠1 = m∠2[tex]{}[/tex] 3. Subtraction property
4. ∠1 ≅ ∠2 [tex]{}[/tex] 4. Definition of congruency
What are congruent angles?Two angles are congruent if the measures of the each angle are equivalent.
The details of the reasons used to prove that ∠1 = ∠2, are as follows;
Linear pair angles
Linear pair angles are adjacent angles that have a common side and for which the other non common sides of the two angles, together form a straight line.
Substitution property
The substitution property of equality states that if a = b then b can replace a in any expression or equation, with the value of the new expression remaining the same as the previous expression or both sides of the new equations remain equivalent.
Subtraction property
The subtraction property of equality states that the subtraction of the same amount from two quantities that have the same amount, will result in two new quantities that remain equivalent.
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Scientists have found a way to distinguish chronic-fatigue syndrome (CFS) from post-treatment Lyme disease by different proteins in a patient's spinal fluid. In a study of 3991 patients, the results to the right were found.
1538 had the protein for normal patients, CFS, and post-treatment Lyme disease;
1884 had the protein for CFS and Lyme;
408 had the protein for CFS only;
2602 had the protein for CFS;
1731 had the normal protein as well as the one for Lyme;
2798 had the protein for Lyme;
2516 had the normal protein.
Part 1
(a) There were ---- patients who only had the protein for Lyme.
(Type a whole number.)
Part 2
(b) There were ---- patients who only had the normal protein.
(Type a whole number.)
Part 3
(c) There were ---- patients who had none of the proteins.
Answer:
Part 1
(a) There were 2798 patients who only had the protein for Lyme.
Part 2
(b) There were 2516 patients who only had the normal protein.
Part 3
(c) It is not specified in the given information how many patients had none of the proteins. It is only specified that 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease; 1884 had the protein for CFS and Lyme; 408 had the protein for CFS only; 2602 had the protein for CFS; 1731 had the normal protein as well as the one for Lyme; 2798 had the protein for Lyme; 2516 had the normal protein. Based on this information, it is not possible to know how many patients had none of the proteins.
Answer: There are no patients who had none of the proteins.
Step-by-step explanation: Part 1
(a) There were 408 patients who only had the protein for Lyme.
This information can be inferred from the data given: 1884 had the protein for CFS and Lyme, and 2798 had the protein for Lyme. If we subtract 1884 from 2798, we get 914 which is the number of patients who only had the protein for Lyme.
Part 2
(b) There were 2516 patients who only had the normal protein.
This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, and 2602 had the protein for CFS. If we add 1538, 1884 and 2602, we get 6124, then if we subtract 6124 from the total number of patients (3991) we get 2516 patients who only had the normal protein.
Part 3
(c) There were 0 patients who had none of the proteins.
This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, 408 had the protein for CFS only, 2602 had the protein for CFS, 1731 had the normal protein as well as the one for Lyme, 2798 had the protein for Lyme, and 2516 had the normal protein. All patients have at least one protein, therefore there are no patients who had none of the proteins.
find the charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s].
The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is given by q(t) = q0 + (t)I,
The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is calculated by the formula q(t) = q0 + (t)I, where q0 is the initial charge and I is the current.
The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is given by q(t) = q0 + (t)I, where q0 is the initial charge and I is the current. To calculate q(t), we need to first calculate the initial charge q0 and then calculate the current I. To calculate q0, we need to integrate the current I over the time interval (0, t). To calculate q(t), we need to know q0 and I. Then, we can calculate q(t) by multiplying t by I and adding it to q0. For example, if q0 = 3 C and I = 2 A, then q(t) = 3 + (t)(2) = 3 + 2t C.
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Fill in the blank. The symbol C represents a constant. Write this result as a linear first-order differential equation that is free of the symbol C1 and has the form dy/dx f(x, y)
The solution for the given differential equation is [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex].
We have given a differential equation:
[tex]\frac{d}{dx}(C_1e^{12x})[/tex]
since C1 is a constant,
=[tex]C_1\frac{d}{dx} (e^{12x})[/tex]
we know that [tex]\frac{d}{dx} (e^{ax}) = e^{ax}\frac{d}{dx} (ax)[/tex]
= [tex]C_1e^{12x}(12) = 12C_1e^{12x}[/tex]
Therefore, [tex]\frac{d}{dx}(C_1e^{12x}) = 12C_1e^{12x}[/tex]
Now, let y = [tex]C_1e^{12x}[/tex]
Therefore, [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex]
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The complete question is:
Fill in the blank. The symbol C represents a constant. [tex]\frac{d}{dx}C_1e^{12x}[/tex]= ____ Write this result as a linear first-order differential equation that is free of the symbol C1 and has the form dy/dx = f(x, y).
initially, there were the same number of blue marbles and red marbles in a bag. John took out 5 blue marbles and there were twice as many red marbles as blue marbles in the bag. How many red marbles are there in the bag?
Step 2: Identify the words in the problem that translate into mathematical actions.
Choose one or more:
A. more
B. of
C. and
D. if
The words that can be changed into mathematical or arithmetic operators are
More = +, of = *, if=Condition.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.
The four basic arithmetic operations in Maths, for all real numbers, are:
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
Now,
we can change
More = +, of = *, if=Condition as only these makes sense according to mathematics actions.
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Divide if possible. 36,000 divided 90 (Type whole numbers)
A. The quotient is with no remainder ( type a whole number )
B. The quotient is with remainder .
C. The quotient is undefined
f(x)/g(x)= (x+26)/(14x^2+42x)
Domain restriction for f(x)/g(x) is
x ≠
The domain restriction for f(x)/g(x) is x ≠ 0 or -3
How to find the domain restriction for f(x)/g(x)?The domain of a function is the set of all input values (or "independent variable") for which the function is defined and produces a valid output (or "dependent variable").
In other words, it is the set of all valid input values for which the function will produce a real output and not give an error or undefined result.
But the domain restriction is the set of values that are not allowed as input for the function.
f(x)/g(x) = (x+26)/(14x²+42x)
In order to find the Domain restriction for f(x)/g(x), equate the denominator g(x) to zero and solve for x. That is:
14x²+42x = 0
14x(x + 3) = 0
14x = 0 or x + 3 = 0
x = 0 or x = -3
Thus, the Domain restriction is x ≠ 0 or -3
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Giving brainliest! Pls and ty
The experimental probability that the puppy would be named lemon or linus is 13/50. Option D
How to solve the probabilityThe experimental probability that the pupply would be named lemon or linus can be solved by
P(A) + P(B)
where P (A) is probability of lemon
P(B) is probability of linus
The total value in the frequency table is given as 10 + 13 + 3 + 14 + 10 = 50
P(A) = 3 / 50
P(B) = 10 / 50
The probability = 3/50 + 10/50
solve using the lcm method of solving fractions. There is a common denominator
3 + 10 / 50
= 13 / 50
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A tree is 6 feet 11 inches tall. How tall is it in inches?
in
Answer: 83 inches
Step-by-step explanation:
1. 12 inches = 1 foot
2. 12x6=72 inches
3. 72+11=83 inches
Cognitive psychology question.
Signal Detection
1) How are hit and miss related? How are false alarms and correct rejection related? Explain their relationships mathematically.
Simon Effect
1) How would you design a task demonstrating the auditory version of the Simon effect?
The answers include the following below:
If the signal is present the person can decide that it is present or absent and the outcomes are called hits and misses.If the signal is absent the person can still decide that the signal is either present or absent which are called false alarms or correct rejections respectively therefore false alarms = correct rejection. A task demonstrating the auditory version of the Simon effect will be putting the hands close to or far from the loudspeakers.What is Simon effect?The Simon effect refers to the finding that people are faster and more accurate when responding to stimuli that occur in the same relative location as the response.
An appropriate task demonstrating the auditory version of the Simon effect will be putting the hands close to or far from the loudspeakers and noting how fast they react to the stimuli.
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use scenario 3-8. which of the following statements can be made on the basis of the computer output? group of answer choices 69.7% of the variation in fish length can be accounted for by the linear regression of egg production on fish length. 83.5% of the variation in egg production can be accounted for by the linear regression of egg production on fish length. 83.5% of the variation in fish length can be accounted for by the linear regression of egg production on fish length. 69.7% of the variation in egg production can be accounted for by the linear regression of egg production on fish length. 68.4% of the variation in fish length can be accounted for by the linear regression of egg production on fish length.
The computer output for scenario 3-8 indicates that 83.5% of the variation in egg production can be accounted for by the linear regression of egg production on fish length, while 69.7% of the variation in fish length can be accounted for by the same linear regression.
This indicates that there is a strong and significant correlation between fish length and egg production, with egg production increasing as fish length increases. This suggests that egg production is a good predictor of fish length and vice versa, and that changes in one can be used to predict changes in the other.
However, it is worth noting that this correlation is not perfect and that there is still a considerable amount of variation in each that cannot be explained by the linear regression.
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Correct question should be:
Use Scenario 3-8. Which of the following statements can be made on the basis of the computer output?
A. 83.5% of the variation in egg production can be accounted for by the linear regression of
egg production on fish length.
B. 69.7% of the variation in egg production can be accounted for by the linear regression of
egg production on fish length.
C. 83.5% of the variation in fish length can be accounted for by the linear regression of egg
production on fish length.
D. 69.7% of the variation in fish length can be accounted for by the linear regression of egg
production on fish length.
E. 68.4% of the variation in fish length can be accounted for by the linear regression of egg
production on fish length.
What is the limit of the function?
Select True or False for each limit statement
Answer:
The answers are
False
True
True
Thank you
answer the following questions about the proton. location in atom charge 1 elementary charge approximate massture or false
The Complete statement is : The location of proton in the atom is inside nucleus , has a charge of +1 elementary charge and the approximate mass of proton is 1.00727647 amu .
The Protons are the positively charged particles, the electrons are negatively charged particles and the neutrons have no charge.
In an atom there are equal number of protons and number of electrons . Thus the atom is electrically neutral in nature. The charge of the proton is equal and opposite of an electron. So , proton has a unit positive charge.
The Protons are found inside the nucleus of atom , the proton carries the elementary charge of 1.00727647 amu (atomic mass units) , the charge on the proton is +1 .
The given question is incomplete , the complete question is
Answer the following questions about the Proton ,
The location of proton in the atom is ______ , has a charge of ______ elementary charge and the approximate mass of proton is _____ amu .
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For which data set are the mean, median, and mode the same value?
4, 8, 8, 8, 4
4, 8, 6, 8, 4
4, 8, 6, 6, 6
8, 6, 4, 8, 6
Answer:
Step-by-step explanation:
the answer is : 4,8,6,6,6
= 6
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 51 ounces and a standard deviation of 10 ounces.
Answer: The statement given tells us that the Acme Company manufactures widgets and that the distribution of widget weights is bell-shaped. A bell-shaped distribution is also known as a normal distribution or a Gaussian distribution. This means that the majority of the data will cluster around the mean (average) value and the farther the data is from the mean, the less common it is.
The mean weight of the widgets is given as 51 ounces, which is the average weight of all the widgets manufactured by the company. The standard deviation is given as 10 ounces, which is a measure of how spread out the data is from the mean. A smaller standard deviation means that the data is more tightly clustered around the mean, while a larger standard deviation means that the data is more spread out.
This information allows us to make some predictions about the weights of the widgets. For example, we know that approximately 68% of the widgets will weigh between 41 ounces (mean - standard deviation) and 61 ounces (mean + standard deviation). Additionally, we know that approximately 95% of the widgets will weigh between 31 ounces (mean - 2standard deviation) and 71 ounces (mean + 2standard deviation) and 99.7% of the widgets will weigh between 21 ounces (mean - 3standard deviation) and 81 ounces (mean + 3standard deviation).
It is important to note that these predictions are based on the assumption that the distribution of widget weights is indeed bell-shaped. If that assumption is not true, these predictions may not be accurate.
Step-by-step explanation:
Identify the type of observational study A researcher plans to obtain data by interviewing spouses of victims who perished in a tsunami. He will interview them, and people unrelated to the victims, over the next 10 years to see how closeness to a traumatic event might affect recovery time. Choose the correct type of observational study below. â“”A. prospective B. retrospective O C. cross-sectional
The type of observational study in the following scenario is considered as prospective study.
A prospective study, also known as a prospective cohort study, is a type of longitudinal study in which researchers follow and watch a group of individuals across time to collect data and track the development of outcomes. A prospective study is one that follows participants over time to see if certain outcomes, like the onset of a disease, occur and then compares those instances to any known or suspected risk or protective factors (s). It is common practice to follow a group of people, or a "cohort," for an extended period of time as part of the study. In this scenario, the researcher wants to learn how closeness to a traumatic event might effect healing time by conducting interviews with victims and witnesses over the next 10 years. Hence, it fits the criteria for a prospective observational study.
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(3x^4+10×^3-2×^2+28×+27)÷(×+4)
Answer:
Step-by-step explanation: 21
based upon the data presented in the graph, which of the following best identifies the highest wolf population size?
The graph shows a maximum wolf population size of 500 individuals, which occurred in 2017.
The graph depicts the magnitude of the wolf population in a certain location during the previous 25 years. The population size is shown to have changed over time, with the peak population count of 500 people happening in the year 2017. A population size of 450 people, which is a little less than the highest population level, was then reached in 2018. The year 2000 saw the lowest population size, with only 200 people living there. In 2017, there were 500 people in the population, which had grown considerably over the years. This suggests that over the past 25 years, the wolf population has been growing which occurred in 2017.
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The complete question is
based upon the data presented in the graph, which of the following best identifies the highest wolf population size which occurred in 2017?
PLS HELP ITS MY BDAY TOMORROW
Jay measured the lengths of 16 fish.
Use the graph below to estimate the lower
and upper quartiles of the lengths.
Cumulative frequency
20-
18-
16-
14-
12-
10-
8-
6-
4-
+ NO
2-
0
-10
Lengths of fish
10 15 20 25 30 35 40
Length (inches)
Answer:
lower quartile: 10upper quartile: 25Step-by-step explanation:
You want to use the graph to estimate the lower and upper quartiles of the lengths of the 16 fish that Jay measured.
QuartilesThe lower quartile is comprised of the 1/4 of the total number of fish that are the shortest. The graph shows that 4/16 of the fish are 10 inches or less, so the lower quartile is 10 inches.
The upper quartile is comprised of the 1/4 of the total number of fish that are the longest. The graph shows that 12/16 of the fish are 25 inches or less, so 4/16 of the fish are 25 inches or more. The upper quartile is 25 inches.
The lower and upper quartiles are 10 inches and 25 inches, respectively.
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Please help I only got 20 minutes left for class
Answer:
D is the answer..
Step-by-step explanation:
Brice is taking a bike tour of the city. The entire tour is 24 7/10 kilometers long. Brice knows that his average biking rate is 4.3 meters per second. A. What is Brice's biking rate in kilometers per hour? B. About how long will it take Brice to complete the biking tour? Express your answer in hours and minutes. C. Explain how you know your answer is reasonable. Please show all work.
The speed in kilometers per hour is 15.48. And the total number of hours for the trip will be 1.60 hours.
What is an average speed?The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.
We know that the average speed formula is given as,
Average speed = Total distance / Total time
Brice is taking a bike tour of the city. The entire tour is 24 ⁷/₁₀ kilometers long. Brice knows that his average biking rate is 4.3 meters per second.
Convert the mixed fraction number to a decimal number. Then we have
24 ⁷/₁₀ = 24 + 0.70
24 ⁷/₁₀ = 24.70 kilometers
Convert the speed into kilometers per hour. Then we have
Speed = 4.3 x 18/5
Speed = 15.48 kilometers per hour
Then the total number of hours for the trip is given as,
15.48 = 24.70 / T
T = 24.70 / 15.48
T = 1.60 hours
The speed in kilometers per hour is 15.48. And the total number of hours for the trip will be 1.60 hours.
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The graph of a cubic polynomial function
has horizontal tangent lines at (1, −2) and (−1, 2). Find
an equation for the function and sketch its graph.
Answer: A cubic polynomial function has the form f(x) = ax^3 + bx^2 + cx + d.
A horizontal tangent line is a line that is parallel to the x-axis and it occurs at a critical point of the function, where the derivative of the function is 0.
We know that a cubic function has 3 critical points and thus 3 derivative that could be 0, so to find the equation of the cubic function we will use these two points to find the value of a, b, c, and d.
We know that the critical points of a cubic function are found by solving f'(x) = 0, where f'(x) is the derivative of the function, so we have:
f'(x) = 3ax^2 + 2bx + c = 0
Now we can use the two points to find the value of a, b, c, and d.
We know that the point (1,-2) is on the graph of the function, so we can substitute it into the equation to find d:
f(1) = a + b + c + d = -2
And we know that the point (-1,2) is on the graph of the function, so we can substitute it into the equation to find d:
f(-1) = -a + b - c + d = 2
Now we can use these two equations to find the value of a, b, and c:
a + b + c + d = -2
-a + b - c + d = 2
2a + 2d = 0
a = -d
-a + b - c + d = 2
b - c = 4
3ax^2 + 2bx + c = 0
3(-d)x^2 + 2bx - c = 0
Now we can use these equations and the critical points to find the value of a, b, c, and d
3(-d)x^2 + 2bx - c = 0, (1,-2) => 3d+2b-c = 0
3(-d)x^2 + 2bx - c = 0, (-1,2) => 3d-2b+c = 0
b-c = 4
Solving these equations, we have:
a = -1/3
b = 1
c = -5/3
d = -2
And the equation for the function is:
f(x) = -1/3x^3 + x^2 - 5/3x - 2
We can now sketch the graph of the function by using the information that we have. The cubic function will have an vertex of symmetry at (0,-2) and two horizontal tangent lines at (1,-2) and (-1,2) .
Since a < 0, the function is concave down, so the graph will be opened downwards and will have a local minimum at (0,-2) .
It is important to note that this is one possible equation for a cubic function that has horizontal tangent lines at (1, −2) and (−1, 2), but there may be other possibilities.
Step-by-step explanation:
I need help i dont get it there is more on the second one but I coundent get it on the thing
1) Note that the result of the above highlighted 10 by 10 block of units in the fraction are:
10/100; and
1/ 10.
2) In decimal, that would be:
0.1
3) In part-to-part ratio it would be:
10:90
4) In Part to whole ratio 10/100
5) In whole to part, that would be:
100:10
5) In percent, that would be 10%
A part-to-whole ratio compares a part to the total of all parts. For example, if you have 100 apples and you want to know what percentage of them are red, you would express the number of red apples as a ratio of the total number of apples. In this case, 10 red apples would be expressed as a ratio of 10:100
A part-to-part ratio compares two or more quantities in terms of their relative sizes. For example, if you have 100 apples and you want to know how many more red apples than green apples you have, you would express the number of red apples and the number of green apples as a ratio of each other. In this case, if you have 30 red apples and 20 green apples, the ratio would be 30:20
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Find JK.
12
2
I
J
K
30°
Write your answer in simplified, rationalized form. Do not round.
JK =
If the series JK has 12 2 I J K 30, the value of JK is 720
How do we determine the value?In order to find the value of JK, multiply the given values all through and then generate the answer in a simplified manner
JK=(12)(2)(30)
Multiply all the figures
JK = 12 X 2 X 30
JK = 720
Therefore, the correct answer is as given above. It can be concluded that the value of JK is 720 as a result of the multiplication.
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A grocery store is placing an order for dairy products. there are 8 varieties of dairy products sold in cases, where each case contains all the same variety of dairy products. the store will order 50 cases in total. 1) How many ways are there to place the order? 2)one of the varieties of dairy products is milk. how many ways are there to place the order if they order at most 20 cases of milk
We have 50 cases to distribute among 8 varieties of dairy products, with a restriction of 20 cases of milk.
How find the total number?To find the total number of ways to place the order, you can use the binomial coefficient formula, which is often used in combinatorics to count the number of ways to choose k items from a set of n items without regard to order. In this case, you have 8 varieties of dairy products and you want to choose 50 cases in total, with no regard to the order in which you choose the cases. So, the number of ways to place the order is:
(n k) = (8 50) = 8! / (50! (8-50)!) = 8! / (50! (-42)!) = 8! / 50! = 87654321 / (50494847464544434241)
This is a very large number, and it's impractical to calculate it exactly.
To find the number of ways to place the order if they order at most 20 cases of milk, you can use a similar approach, but with a restriction on the number of cases of milk. One way to do this is to use the stars and bars method, which is a combinatorial method for counting the number of ways to distribute n identical items into k distinguishable containers, with a restriction on the number of items in some of the containers.
In this case, we have 50 cases to distribute among 8 varieties of dairy products, with a restriction of 20 cases of milk. So, the number of ways to place the order is:
(50 + 8 - 1) choose (8 - 1) = 56 choose 7 = 56! / (7! 49!) = 56555453525150 / (7654321) = 807,794,400
This is the number of ways to place the order if they order at most 20 cases of milk.
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Find an equation of a circle that satisfies the given conditions. Center at the origin, passes through (7, 8)
The equation of a circle whose center is at the origin and passes through (7, 8) is x² + y² = 113
Circle is a round geometry whose all points constitute form a path having a constant distance (radius) from a fixed point (center of the circle).
The standard form for the equation of a circle is (x − h)² + (y − k)² = r², where (h,k) is the center of the circle, and r is the radius.
Center = (h,k) = (0,0)
Point = (7,8)
Now we input those values into the equation:
(x − h)² + (y − k)² = r²
(x − 0)² + (y − 0)² = r²
x² + y² = r²
Next, we have to determine the radius. It can be done by applying Pythagoras' Theorem. Look at the picture:
x² + y² = r²
7² + 8² = r²
49 + 64 = r²
113 = r²
Then we go back to the previous equation, and we get:
x² + y² = r²
x² + y² = 113
Thus, the equation of a circle whose center is at the origin and passes through (7, 8) is x² + y² = 113
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How many numbers did Jane write?
Jane wrote all the natural numbers from m to k (where k>m).
Answer:
k-m+1
if you have 36 and 78 for example, you would do 78-36 to find how many numbers there are plus one. so, the answer is k-m+1
Jane typed all the natural numbers between m and k (where k>m), which implies she wrote all the positive integers between m and k, inclusive. Jane would have written the numbers 5, 6, 7, 8, 9, and 10 if m was 5 and k was 10.
What are natural numbers?Natural numbers are positive integers (1, 2, 3, and so on) that can be counted and ordered. They are the most fundamental sort of number in mathematics and are frequently referred to as counting numbers. Natural numbers begin with one and continue forever; however, they do not include negative numbers, fractions, or decimals.
Natural numbers are the foundation of many mathematical ideas and are used to express the quantities of things in a collection. Natural numbers, for example, are used to define the number of sides of a polygon, the dimensions of a matrix, and the length of a number line. They are also used to indicate how much time has elapsed.
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A company offers ID theft protection using leads obtained from client banks. Three employees work 40 hours a week on the leads, at a pay rate of $18 per hour per employee. Each employee identifies an average of 4,000 potential leads a week from a list of 4,800. An average of 7 percent of potential leads actually sign up for the service, paying a one-time fee of $90. Material costs are $1,300 per week, and overhead costs are $8,800 per week.
Calculate the multifactor productivity for this operation in fees generated per dollar of input.(Round your answer to 2 decimal places.)
The multifactor productivity for a given operation is 6.16 fees generated per dollar of input.
What is Break Even Point?The Break Even Point, or the inflection point at which a corporation starts to make a profit, is the amount of output required for a company's revenue to equal its total costs.
First, we need to calculate the revenue generated per week:
Potential leads per week = 3 employees x 4,000 leads/employee/week = 12,000 leads/week
Actual sign-ups per week = 12,000 leads/week x 7% = 840 sign-ups/week
Revenue per week = 840 sign-ups/week x $90/sign-up = $75,600/week
Next, we need to calculate the input costs per week:
Labor cost per week = 3 employees x $18/hour x 40 hours/week/employee = $2,160/week
Material cost per week = $1,300/week
Overhead cost per week = $8,800/week
Total input cost per week = $2,160/week + $1,300/week + $8,800/week = $12,260/week
Finally, we can calculate the multifactor productivity:
Multifactor productivity = Revenue per week / Input cost per week = $75,600/week / $12,260/week = 6.16
So the multifactor productivity for this operation is 6.16 fees generated per dollar of input.
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