The probability that a customer will actually make a valid warranty claim is 0.075.
What is Probability?A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
According to question:The probability that a customer will make a valid warranty claim is the probability that the customer both uses the bike in the first year (which has a probability of 0.75) and discovers a defect (which has a probability of 0.10).
Using the multiplication rule of probability, the probability that both of these events occur is:
0.75 x 0.10 = 0.075
Therefore, the probability that a customer will actually make a valid warranty claim is 0.075.
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mr.woodstock has a plot of land 36 meter long and 16 meters wide. he uses the land for mixed farming- rearing animals and growing crop? What length of wire does mr.woodstock need to fence his land?
Mr. Woodstock will need to purchase 144 meters of wire to fully encircle his land. He will need to measure the length of the four sides of the land and add them together. The four sides measure 36 meters + 36 meters + 16 meters + 16 meters, which equals a total of 104 meters. He should buy enough wire to cover an additional 40 meters to account for any extra material he may need. Therefore, he needs to purchase 144 meters of wire for his fencing.
olivia and kieran share money in the ratio 2:5. Olivia gets £42. how much did kieran get?
[tex] \huge \: \tt \green{Answer} [/tex]
Olivia and kieran share ratio 2 : 5
[tex] \texttt{olivia's share \: of \: money = £42 }= \frac{2}{7} \\ [/tex]
Total Amount of Money = Olivia's share of money × Reciprocal of olivia's share
[tex] \tt \: = > 42 \times \frac{7}{2} \\ \\ = > 147[/tex]
Kieran's share of Money =
[tex] = > 147 \times \frac{5}{7} \\ \\ = > \sf{ \pink{£105}}[/tex]
My question is the picture
Answer:
B. A student was most likely to have summer as their favorite season, whether or not they have allergies
Step-by-step explanation:
If you look at the chart. There is a majority under the summer column. Both those who have and don't have allergies favor summer.
Really need help asap !
The value of h(x) using exponents are as follows:
For -1, the value of h(x)=1/10
For 0, the value of h(x) = 1
For 1, the value of h(x) = 10
For 2, the value of h(x) = 100
For 3, the value of h(x) = 1000
What are exponents?The exponent of a number tells us how many times the original value has been multiplied by itself. For instance, 2×2×2×2 can be expressed as [tex]2^{4}[/tex] the result of 4 times multiplying 2 by itself. Thus, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."
Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times. Here x is the base and n is the power.
Now here, as we put the value of x in the equation, h(x) we can get the value of h(x) for each value of x.
So,
For -1, the value of h(x)=1/10
For 0, the value of h(x) = 1
For 1, the value of h(x) = 10
For 2, the value of h(x) = 100
For 3, the value of h(x) = 1000
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1. A car dealer bought 10 different cars which cost him 5, 3, 2, 6, 7, 2, 3, 9, 3, and 4 thousand euros respectively. a. Find the mean, median, and mode price of the cars he bought b. How will the mean, median, and mode be affected if the dealer sells the cars at a price of 20% more than what he bought each one? c. If each buyer pays an additional amount of 1000 euros for transfer fees, how the answers of part (b) will be affected?
a) The mean, median, and mode price of the cars bought by the car dealer are:
Mean = Euro 4,400Median = Euro 3,500Mode = Euro 3,000.b) If the car dealer sells the cars for 20% more than the purchase prices, the mean, median, and mode prices will increase to:
Mean = Euro 5,280Median = Euro 4,200Mode = Euro 3,600.c) With the payment of an additional Euro 1,000 as transfer fees, the mean, median, and mode prices will increase to:
Mean = Euro 6,280Median = Euro 5,200Mode = Euro 4,600.What are the mean, the median, and the mode?The mean is the quotient of the total value divided by the number of items in the data set. It is also known as the average.
The median is the middle value in an ordered list (ascending or descending).
On the other hand, the mode is the value that occurs most often in the data set.
The prices of different cars:
Car 1 = Euro 5,000
Car 2 = Euro 3,000
Car 3 = Euro 2,000
Car 4 = Euro 6,000
Car 5 = Euro 7,000
Car 6 = Euro 2,000
Car 7 = Euro 3,000
Car 8 = Euro 9,000
Car 9 = Euro 3,000
Car 10 = Euro 4,000
Total value = Euro 44,000
Mean = Euro 4,400 (Euro 44,000/10)
Mode = Euro 3,000
Median = Euro 3,500 (Euro 3,000 + Euro 4,000)
b) Markup = 20%
Cost price = 100%
Selling price = 120% (100 + 20)
Mean = Euro 5,280 (Euro 4,400 x 1.2)
Median = Euro 4,200 (Euro 3,600 x 1.2)
Mode = Euro 3,600 (Euro 3,000 x 1.2)
c) Additional Transfer Fees of Euro 1,000:
Mean = Euro 6,280 (Euro 4,400 x 1.2 + Euro 1,000)
Median = Euro 5,200 (Euro 3,600 x 1.2 + Euro 1,000)
Mode = Euro 4,600 (Euro 3,000 x 1.2 + Euro 1,000)
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a rectangle is dilated by a scale factor of 2/3 about the center of the origin. what should the area of the pre-image be?
Answer:
Step-by-step explanation:
kbggfdtddcsfbdfserenis amazing
show that the properties of a probability distribution for a discrete random variable are satisfied.
The properties of a probability distribution for a discrete random variable ensure that the probabilities assigned to each possible value of the variable are consistent with the axioms of probability and allow for meaningful inference and prediction.
The properties of a probability distribution for a discrete random variable are.
The probability of each possible value of the random variable must be non-negative.
The sum of the probabilities of all possible values must equal 1.
The probability of any event A is the sum of the probabilities of the values in the sample space that correspond to A.
These properties are satisfied because the probabilities of each possible value of a discrete random variable are defined in such a way that they are non-negative and sum to 1. Additionally, any event A can be expressed as a collection of possible values of the random variable, and the probability of A is then computed as the sum of the probabilities of those values.
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can someone help me? please
evalute the following function h(x)=3x2+ax-1 for h(3) and find the value for a.
Answer:
Step-by-step explanation:
[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]
But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.
what is the Taylor's series for 1+3e^(x)+x^2 at x=0
The Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] is :
[tex]1 + 3e^x+ x^2 = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
What do you mean by Taylor's series ?
The Taylor's series is a way to represent a function as a power series, which is a sum of terms involving the variable raised to increasing powers. The series is centered around a specific point, called the center of the series. The Taylor's series approximates the function within a certain interval around the center point.
The general formula for the Taylor's series of a function f(x) centered at [tex]x = a[/tex] is:
[tex]f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...[/tex]
where [tex]f'(a), f''(a), f'''(a),[/tex] etc. are the derivatives of f(x) evaluated at [tex]x = a[/tex].
Finding the Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] :
We need to find the derivatives of the function at [tex]x=0[/tex]. We have:
[tex]f(x) = 1 + 3e^x + x^2[/tex]
[tex]f(0) = 1 + 3e^0 + 0^2 = 4[/tex]
[tex]f'(x) = 3e^x+ 2x[/tex]
[tex]f'(0) = 3e^0 + 2(0) = 3[/tex]
[tex]f''(x) = 3e^x + 2[/tex]
[tex]f''(0) = 3e^0 + 2 = 5[/tex]
[tex]f'''(x) = 3e^x[/tex]
[tex]f'''(0) = 3e^0 = 3[/tex]
Substituting these values into the general formula for the Taylor's series, we get:
[tex]f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...[/tex]
[tex]f(x) = 4 + 3x + 5x^2/2 + 3x^3/6 + ...[/tex]
Simplifying, we get:
[tex]f(x) = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
Therefore, the Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] is :
[tex]1 + 3e^x+ x^2 = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
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the height y in feet of a ball thrown at a child
a) The initial height is 5 feet.
b) The maximum height is 17 feet.
c) The horizontal displacement is 26.3 feet
How high is the ball when it left the childs hands?The height of the ball is modeled by the given quadratic equation:
y = (-1/12)x² + 2x + 5
The ball leaves the child's hands at the beginning, so to get the height at that point we just need to evaluate this in x = 0, we will get:
y = (-1/12)*0² + 2*0 + 5
y = 5
The height is 5 feet.
b) To get the maximum height we need to find the vertex, in this case the vertex is at:
x = -(2/2)*-12 = 12
Then the maximum height is:
y = (-1/12)*12² + 2*12 + 5 = 17 feet.
Lastly, the ball will hith the ground when y = 0, then we need to solve:
(-1/12)*x² + 2x + 5 = 0
x² -12*2x - 12*5 = 0
x² -24x - 60 = 0
The quadratic formula gives:
[tex]x = \frac{24 \pm \sqrt{(-24)^2 -4*1*-60} }{2}[/tex]
The positive solution gives:
x = 26.3
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Let the Universal Set, S, have 158 elements. A and B are subsets of S. Set A contains 67 elements and Set B contains 65 elements. If Sets A and B have 9 elements in common, how many elements are in neither A nor B?
There are 92 elements in A but not in B.
What are sets?In mathematics, a set is a well-defined collection of objects or elements. Sets are denoted by uppercase symbols, and the number of elements in a finite set is denoted as the cardinality of the set enclosed in curly braces {…}.
Empty or zero quantity:
Items not included. example:
A = {} is a null set.
Finite sets:
The number is limited. example:
A = {1,2,3,4}
Infinite set:
There are myriad elements. example:
A = {x:
x is the set of all integers}
Same sentence:
Two sets with the same members. example:
A = {1,2,5} and B = {2,5,1}:
Set A = Set B
Subset:
A set 'A' is said to be a subset of B if every element of A is also an element of B. example:
If A={1,2} and B={1,2,3,4} then A ⊆ B
Universal set:
A set that consists of all the elements of other sets that exist in the Venn diagram. example:
A={1,2}, B={2,3}, where the universal set is U = {1,2,3}
n(A ∪ B) = n(A – B) + n(A ∩ B) + n(B – A)
Hence, There are 92 elements in A but not in B.
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In a poll conducted by the Gallup organization 16% of adult, employed Americans were dissatisfied with the amount of vacation time. You conduct a survey of 500 adult, employed Americans.
(3 points) Using the binomial formula (or technology) – find the probability that less than 70 are dissatisfied with their vacation time.
(2 points) Show that this distribution can be approximated by the normal distribution.
(5 points) Use the normal curve to approximate the probability that less than 70 are dissatisfied with their vacation time.
The probability that less than 70 are dissatisfied with their vacation time is approximately 0.000008.
The normal distribution can be used to approximate this binomial distribution.
The probability that less than 70 are dissatisfied with their vacation time is approximately 0.0082, using the normal curve approximation.
How to Solve the Probability?Using the binomial formula:
n = 500
p = 0.16
q = 1 - p = 0.84
We want to find P(X < 70), where X is the number of people out of 500 who are dissatisfied with their vacation time.
P(X < 70) = Σi=0^69 (500 choose i) * 0.16^i * 0.84^(500-i)
Using technology, we can find this probability to be approximately 0.000008.
To show that this distribution can be approximated by the normal distribution, we need to check if the conditions for the normal approximation are met:
np = 500 * 0.16 = 80 ≥ 10
nq = 500 * 0.84 = 420 ≥ 10
Since both conditions are met, we can use the normal distribution to approximate this binomial distribution.
To use the normal curve to approximate the probability that less than 70 are dissatisfied with their vacation time, we need to standardize the binomial distribution:
μ = np = 80
σ = sqrt(npq) = sqrt(500 * 0.16 * 0.84) ≈ 4.58
We want to find P(X < 70), which is equivalent to finding the probability that a standard normal variable Z is less than (69.5 - 80) / 4.58 = -2.37.
Using a standard normal table or technology, we find this probability to be approximately 0.0082.
Therefore, the probability that less than 70 are dissatisfied with their vacation time is approximately 0.0082, using the normal curve approximation.
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All of the following statements related to sample size are true characteristics of qualitative methodology except for which of the following?
The statement based on sample size representing true characteristics of qualitative methodology are smaller sample size, qualitative research and theoretical research of qualitative data.
Some general statements about sample size in qualitative methodology are as follow,
Qualitative research typically involves smaller sample sizes than quantitative research.
The sample size in qualitative research is not determined by statistical power calculations.
But rather by theoretical saturation and the quality of data collected.
The goal of qualitative research is to gain a deep understanding of the phenomenon being studied.
Rather than to generalize findings to a larger population.
Qualitative research often involves purposive or convenience sampling rather than random sampling.
All of these statements are generally true characteristics of qualitative methodology.
If any statement contradicts one of these characteristics,
Then that statement would not be true for qualitative methodology.
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The given question is incomplete, I answer the question in general according to my knowledge:
Write all the statement related to sample size representing true characteristics of qualitative methodology except for which of the following?
FILL IN THE BLANK. If the number of drinks consumed by a small group is 4, 4, 6, 7, and 8, the number 6 would be the _____ for that group.
If the number of drinks consumed by a small group is 4, 4, 6, 7, and 8, the number 6 would be the median for that group.
The median is a measure of central tendency in a set of data, and it represents the middle value of the data set when the values are arranged in order. To find the median of a set of data, we follow these steps:
Arrange the data in order from smallest to largest (or from largest to smallest).
If the number of data points is odd, the median is the middle value.
If the number of the data points is even, then the median is the average of the two middle values.
For example, if we have the data set {2, 4, 5, 7, 9}, we would arrange it in order to get {2, 4, 5, 7, 9}. Since there are an odd number of data points (5), the median is the middle value, which is 5.
If we have the data set {2, 4, 5, 7, 9, 10}, we would arrange it in order to get {2, 4, 5, 7, 9, 10}. Since there are an even number of data points (6), the median is the average of the two middle values, which are 5 and 7. Therefore, the median is (5 + 7)/2 = 6.
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the formula for converting degrees fahrenheit (F) to degrees Kelvin is K= 5/9 (F = 459.67) Solve for F, terms of K
The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
What is degrees Fahrenheit and degrees Kelvin?Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.
The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.
Given that, K = 5/9 (F - 459.67).
To obtain F in term of K we isolate the value of F as follows:
K = 5/9 (F - 459.67)
Multiplying both sides by 9/5, we get:
(9/5) K = F - 459.67
Adding 459.67 to both sides, we get:
F = (9/5) K + 459.67
Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
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To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±$17.64.
Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
The correct interpretation of the confidence interval is We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27 that is option A.
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.
Given,
Confidence interval, CI = 62.63 +/- 17.64
CI = ( 44.99 , 80.27 )
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.
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Complete question:
To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±$17.64.
Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.We are 95 percent confident that the mean cost of a hospital visit for the parrot owners in the sample is between $44.99 and $80.27.For all parrot owners in the state, 95 percent of hospital visits for parrot care cost between $44.99 and $80.27.There is a 0.95 probability that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.Consider the following algebraic statements and determine the values of x for which each statement is true.
8=-|x|
Answer:
This is false.
Step-by-step explanation:
Since absolute value bars change negatives into positives and positive into themselves (positives) we can put the example:
[tex]-|8|\\[/tex]
When we remove the absolute value bars, 8 will still equal 8. But, we have a negative, therefore the 8 has a negative after being simplified with absolute value.
x = -8, not positive 8.
Answer:
Ther are no values of x that would make this statement true. There is no solution.
Step-by-step explanation:
6TH GRADE MATH FIND SLOPE IN THE EQUATION
Answer:
Step-by-step explanation:
answer is -2
I need help on this one to sorry
Answer:
250 and 250.1
Answer:
250.1
Step-by-step explanation:
5002 divided by 20 equals 250.1
find the slope of a line parallel to the line whose equation is 5x - 6y = 30. fully simplify your answer 
By answering the presented questiοn, we may cοnclude that Since a line equatiοn parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.
What is equatiοn?When twο expressiοns are equal, a mathematical equatiοn is a statement stating that equality. Twο sides are jοined by the algebraic symbοl (=), and tοgether they make up an equatiοn. Fοr instance, the claim that "2x + 3 = 9" means that "2x plus 3" equals the number "9" is made in this argument. Finding the value(s) οf the variable(s) necessary fοr the equatiοn tο be true is the gοal οf sοlving equatiοns.
There are variοus types οf equatiοns, including regular and nοnlinear οnes with οne οr mοre elements. "x² + 2x - 3 = 0" is an equatiοn that raises the variable x tο the secοnd pοwer. Mathematical disciplines like algebra, calculus, and geοmetry all make use οf lines.
the given equatiοn:
[tex]$\begin{array}{c}{{5x-6y=30}}\\ {{-6y=-5x+30}}\\ {{y=(5/6)x-5}}\end{array}$[/tex]
Sο the slοpe οf the given line is 5/6.
Since a line parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.
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by using truth table, find whether the proposition (p ^ q) ^~ (p v q) is a tautology, contradiction, or contingency.
By using the truth table the proposition (p ^ q) ^~ (p v q) represents it is a contingency neither tautology nor contradiction.
To determine whether the proposition (p ^ q) ^~ (p v q) is a tautology, contradiction, or contingency,
Construct a truth table that lists all possible truth values of p and q .
And the resulting truth value of the entire proposition.
Here is the truth table,
p q p v q ~ (p v q) p ^ q (p ^ q) ^ ~ (p v q)
-------------------------------------------------------------
T T T F T F
T F T F F F
F T T F F F
F F F T F T
As we can see from the truth table, there are both True and False results in the final column,
This implies ,
That the proposition (p ^ q) ^~ (p v q) is a contingency, since it is neither a tautology nor a contradiction.
Therefore, using truth table the given proposition is a contingency.
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SOMEONE HELP PLEASE!!!
Find P(C|Y) from the information in the table.
To the nearest tenth, what is the value of P(C|Y)?
A. 0.4
B. 0.5
C. 0.7
D. 0.8
Answer:
The answer to your problem is, B, 0.5
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
As we know that the conditional probability formula of P(A/B) is given by:
P(A/B) = [tex]\frac{P(AnB)}{P(b)}[/tex]
P(C/Y) = [tex]\frac{P(CnY)}{P(Y)}[/tex]
P ( Y ) = [tex]\frac{30}{146}[/tex] and P(CnY) = [tex]\frac{15}{146}[/tex] [ because of the third column shown ]
Thus, the answer is, B. 0.5
Feel free to ask any questions down below \/ !
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
The expression (x < y) && (y == 5) is an alternative way of writing the original expression, and it will be true only if two conditions are met: first, x is smaller than y, and second, y is equal to 5.
The expression !(!(x < y) || (y != 5)) is equivalent to:
(x < y) && (y == 5)
To see why, let's break down the original expression:
!(!(x < y) || (y != 5))
= !(x >= y && y != 5) (by De Morgan's laws)
= (x < y) && (y == 5) (by negating and simplifying)
So, the equivalent expression is (x < y) && (y == 5). This expression is true if x is less than y and y is equal to 5.
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Complete question:
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
(x < y) && (y != 5)
(x >= y) && (y == 5)
(x < y) || (y == 5)
(x >= y) || (y != 5)
Find the measure of ACD
A - 36 degrees
B - 126 degrees
C - 162 degrees
D - 216 degrees
Answer:
C
Step-by-step explanation:
i assume its
C.
Ruhama scores 75, 80, 85 and x in four subjects. For what value of x, Ruhama's average is less than 80?
Answer:
Therefore, for Ruhama's average to be less than 80, the value of x must be less than 80.
Step-by-step explanation:
Let's use the formula for the average (or mean) of a set of numbers: average = (sum of numbers) / (number of numbers)
To find the value of x that makes Ruhama's average less than 80, we need to solve the following inequality:
(75 + 80 + 85 + x) / 4 < 80
Multiplying both sides by 4 gives:
75 + 80 + 85 + x < 320
Simplifying:
x < 320 - 75 - 80 - 85 x < 80
Management estimates that 5% of credit sales are eventually uncollectible. Of the collectible credit sales, 65% are likely to be collected in the month of sale and the remainder in the month following the month of sale. The company desires to begin each month with an inventory equal to 70% of the sales projected for the month. All purchases of inventory are on open account; 30% will be paid in the month of purchase, and the remainder paid in the month following the month of purchase. Purchase costs are approximately 60% of the selling prices. Budgeted January cash payments for December inventory purchases by Collection Corporation are:
Answer:
Step-by-step explanation:
Unfortunately, there is no information provided about the sales projections for the month of January or the selling prices of the inventory. Without this information, it is not possible to calculate the budgeted January cash payments for December inventory purchases.
A company makes a mixture which contains 2% alcohol. If 10 litres of alcohol is added to the mixture, then the concentration increases to 5%. What is the approx. Quantity of the mixture?
A student needs to select 3 books from 3 different math, 3 different physics and 1 history book. What is theProbability that one of them is math and the other two are either physics or history book?
===========================================
Explanation:
There are 3 ways to select the single math book and [tex]4\times3\div2 = 12\div2 = 6[/tex] ways to pick the two other books that are either physics or history (order doesn't matter). This is effectively because we have [tex]3+1 = 4[/tex] books that are either physics or history, and we're using the nCr combination formula.
Overall, there are [tex]3\times6 = 18[/tex] ways to select the three books such that one is math, and the other two are either physics or history.
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There are [tex]3+3+1 = 7[/tex] books total. Since we're selecting 3 of them, we use the nCr formula again and you should get 35.
Or you could note how [tex](7\times6\times5)\div(3\times2\times1) = 210\div6 = 35[/tex]
This says there are 35 ways to select any three books where we can tell the difference between any subject (ie we can tell the difference between the math books for instance).
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We found there are 18 ways to get what we want out of 35 ways to do the three selections. Therefore, the answer as a fraction is 18/35
Use the conclusion of Exercise 15 to establish the following result. If f is analytic and never zero on a domain D, then |/(z)| has no local minima in D. That is, the graph (x, y, |/(x + iy)l) has no "pits."
If f is analytic and never zero on a domain D, then the graph (x,y,|f(x+iy)|) has no "pits". This follows from the fact that Re(f(z)) has no local minima in D.
Exercise 15 establishes the following result: if f is analytic and never zero on a domain D, then the the real part of f(z) has no local minima in D.
To use this result to establish the statement that |f(z)| has no local minima in D, we can use the fact that[tex]|f(z)|=\sqrt{real part of f(z))^2 + \ img part of f(z) )^2[/tex] . Since the sum of two non-negative functions is non-negative, it follows that if the real part of f(z) has no local minima in D, then |f(z)| has no local minima in D either.
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how many irrational numbers are there between 1 and 6 ? individual question 1 3 4 10 infinitely many
There are infinitely many irrational numbers between 1 and 6. This is because between any two distinct rational numbers, there is an infinite number of irrational numbers.
In the case of the interval between 1 and 6, there are infinitely many rational numbers between them, and therefore there must be infinitely many irrational numbers between them as well. This is due to the fact that the set of real numbers is uncountable, meaning that there is no finite or countably infinite list that contains all of its elements.
Thus, the answer is rather a statement about the infinite nature of the set of irrational numbers between 1 and 6.
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