Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2
Answer:
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
Step-by-step explanation:
We have the mean during the interval, which means that the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Lost-time accidents occur in a company at a mean rate of 0.8 per day.
This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.
10 days:
This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]
What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]
[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]
[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]
So
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
Find the domain of the function y = 3 tan(23x)
Answer:
[tex]\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace[/tex].
In other words, the [tex]x[/tex] in [tex]f(x) = 3\, \tan(23\, x)[/tex] could be any real number as long as [tex]x \ne \displaystyle \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right)[/tex] for all integer [tex]k[/tex] (including negative integers.)
Step-by-step explanation:
The tangent function [tex]y = \tan(x)[/tex] has a real value for real inputs [tex]x[/tex] as long as the input [tex]x \ne \displaystyle k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].
Hence, the domain of the original tangent function is [tex]\mathbb{R} \backslash \displaystyle \left\lbrace \left. \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace[/tex].
On the other hand, in the function [tex]f(x) = 3\, \tan(23\, x)[/tex], the input to the tangent function is replaced with [tex](23\, x)[/tex].
The transformed tangent function [tex]\tan(23\, x)[/tex] would have a real value as long as its input [tex](23\, x)[/tex] ensures that [tex]23\, x\ne \displaystyle k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].
In other words, [tex]\tan(23\, x)[/tex] would have a real value as long as [tex]x\ne \displaystyle \frac{1}{23} \, \left(k\, \pi + \frac{\pi}{2}\right)[/tex].
Accordingly, the domain of [tex]f(x) = 3\, \tan(23\, x)[/tex] would be [tex]\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace[/tex].
Can I get help please?
What is the justification for -22-x=14+6x
Answer:
-36/7
Step-by-step explanation:
-22-14=6x+x
-36=7x
-36/7=7x/7
x=-36/7
What is the greatest common factor of 16ab3 + 4a2b + 8ab ?
Answer:
2ab(3b^2+2a+4)
Step-by-step explanation:
6ab^3 + 4a^2b + 8ab
2*3*a*b*b^2 +2*2*a*a*b +2*2*2*a*b
Factor out the common terms
2ab( 3*b^2 +2*a +2*2)
2ab(3b^2+2a+4)
Use all the six numerals 4, 5, 6, 7, 8 and 9 to form two 3-digit even numbers whose sum is smallest, and what is the sum?
9514 1404 393
Answer:
476 +598 = 1074
Step-by-step explanation:
In order for the sum to be smallest, the two most-significant digits must be the smallest possible. That is, they must be 4 and 5.
The two least-significant digits must be even. The remaining even digits are 6 and 8. Then the tens digits are the digits left over: 7 and 9.
Possible sums are ...
476 +598 = 1074
478 +596 = 1074
496 +578 = 1074
498 +576 = 1074
The sum is 1074.
The 7-digit numbers 7123A32, 2B25689 and 450ABC6 are divisible by 3. Find the sum of all possible values of C.
9514 1404 393
Answer:
15
Step-by-step explanation:
For numbers to be divisible by 3, the sum of their digits must be divisible by 3.
This means we require ...
(7 + 1 + 2 + 3 + A + 3 + 2) mod 3 = 0 ⇒ A mod 3 = 0
(2 + B + 2 + 5 + 6 + 8 + 9) mod 3 = 0 ⇒ (2+B) mod 3 = 0 ⇒ B mod 3 = -2
(4 + 5 + 0 + A + B + C + 6) mod 3 = 0 ⇒ (C -2) mod 3 = 0
Possible values of C are 2, 5, 8. Their sum is 15.
_____
For example, let A=0, B=1, C=2. Then we have ...
7123032 = 2374344×3
2125689 = 708563×3
4500126 = 1500042×3
Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data.
The weights of a sample of 100 Maine lobsters.
Answer:
Its quantitive cause its giving a number and quantity/quantitive is for numbers
Answer:
The data is quantitative (because it is asking for measurement or numbers).
Step-by-step explanation:
The second and third I'm not sure how to answer, however,
"A discrete function is a function with distinct and separate values. This means that the values of the functions are not connected with each other. For example, a discrete function can equal 1 or 2 but not 1.5. A continuous function, on the other hand, is a function that can take on any number within a certain interval. For example, if at one point, a continuous function is 1 and 2 at another point, then this continuous function will definitely be 1.5 at yet another point. A continuous function always connects all its values while a discrete function has separations. Now, let's look at these two types of functions in detail."
Hope this helps :)
how did the tempicher change if at first it increased by 5% and then increased by 20 percent
Answer:
Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.
Step-by-step explanation:
Take a number, x.
Now increase it by 5%.
1.05x
Now increase it by 20%.
1.2 * 1.05x = 1.26x
1.26x = 126% of x = 100% of x + 26% of x
100% of x is the same as x, so it is the same as the original x.
The increase is 26% of the original number.
Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.
Evaluate the expression 2x - (4y - 3) + 5xz, when x = -3, y = 2, and z = ‐1.
Answer:
4
Step-by-step explanation:
2x - (4y - 3) + 5xz
Let x = -3, y = 2, and z = ‐1.
2(-3) -( 4(2) -3) +5(-3)(-1)
-6 - (8-3) +15
-6 - 5 +15
-11 +15
4
A box contains 16 large marbles and 18 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 3 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green
Answer:
[tex]P(S&G) =0.7941[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=16+18=>34[/tex]
N0 of Large [tex]L=16[/tex]
N0 of Small [tex]S=18[/tex]
N0 large Green [tex]L_g=9[/tex]
N0 of small White [tex]S_w=3[/tex]
Therefore
Number of green marbles [tex]N0(G)=9+(18-3)[/tex]
Number of green marbles [tex]N0(G)=24[/tex]
Generally the Number of both small and green Marble is
[tex]N0 of (S&G)= 18 - 3 = 15[/tex]
Generally the probability that it is small or green P(S&G) is mathematically given by
[tex]P(S&G) = \frac{(18 + 24 - 15)}{(18 + 16)}[/tex]
[tex]P(S&G) =0.7941[/tex]
whats the next two terms in order are p+q, p , p-q
Answer:
p - 2q and p - 3q
Step-by-step explanation:
A Series is given to us and we need to find the next two terms of the series . The given series to us is ,
[tex]\rm\implies Series = p+q , p , p - q [/tex]
Note that when we subtract the consecutive terms we get the common difference as "-q" .
[tex]\rm\implies Common\ Difference = p - (p + q )= p - p - q =\boxed{\rm q}[/tex]
Therefore the series is Arithmetic Series .
Arithmetic Series:- The series in which a common number is added to obtain the next term of series .
And here the Common difference is -q .
Fourth term :-
[tex]\rm\implies 4th \ term = p - q - q = \boxed{\blue{\rm p - 2q}}[/tex]
Fifth term :-
[tex]\rm\implies 4th \ term = p - 2q - q = \boxed{\blue{\rm p - 3q}}[/tex]
Therefore the next two terms are ( p - 2q) and ( p - 3q ) .
Evaluate
4a^2 x for a = − 2, x = −4
Answer:
4a^2 x for a = − 2, x = −4
Step-by-step explanation:
4a^2 x for a = − 2, x = −4
Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3? in a test plese help fast
Answer:
Graph (a)
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x+ 6} -3[/tex]
Required
The graph
First, calculate y, when x = 0
[tex]y = \sqrt[3]{0+ 6} -3[/tex]
[tex]y = \sqrt[3]{6} -3[/tex]
[tex]y = -1.183[/tex]
The above value of y implies that the graph is below the origin when x = 0. Hence, (c) and (d) are incorrect because they are above the origin
Also, only the first graph passes through point (0,-1.183). Hence, graph (a) is correct
Answer:
the answer is A
Step-by-step explanation:
How do I figure this question out
Answer:
Orthocenter would be in the middle of the shape.
Step-by-step explanation:
B.
Angles tell you how far something has turned from a fix point. The bigger the angle, the bigger the turn. Angles are measured in degrees. Name the four turn
If she is right, the object is worth $25, if she is wrong, the object is worth $4. How high does the probability of the object being authentic have to be for her to take the gamble (meaning purchase the fancy sardine) for $16
Answer:
The expected value for an event with outcomes:
{x₁, x₂, ..., xₙ}
Each one with probability:
{p₁, p₂, ..., pₙ}
Is just:
Ev = x₁*p₁ + ... + xₙ*pₙ
here we have two outcomes:
x₁ = the object worths $25
x₂ = the object is worth $4.
Each one with probability p₁ and p₂ respectively, such that:
p₁ + p₂ = 1
Then the expected value is:
Ev = p₁*($25) + p₂*($4)
Now we want to know how should be the probabilities, such that buying the object for $16 is whort.
Well, the purchase will be whort if the expected value is larger than $16.
This is equivalent to:
p₁*($25) + p₂*($4) - $16 > $0
Knowing that:
p₁ + p₂ = 1
we can rewrite:
p₂ = 1 - p₁
replacing that in the above inequality we get:
p₁*($25) + ( 1 - p₁)*($4) - $16 > $0
Now we can solve this for p₁
p₁*($25 - $4) + $4 - $16 > $0
p₁*$21 - $12 > $0
p₁*$21 > $12
p₁ > $12/$21 = 0.571
The probability of the object being authentic should be larger than 0.571 to take the gamble.
Simplify: (w^3)^8 * (w^5)^5
Answer:
(w^3)^8 * (w^5)^5 = w^49
Step-by-step explanation:
(w^24) * (w^25)
using exponent rule
w^24 • w^25 = w^24+25
w^49
Answer:
Step-by-step explanation:
(W^24)*(W^25)
W^24+25
=W^49
The time it takes a customer service complaint to be settled at a small department store is normally distributed with a mean of 10 minutes and a standard deviation of 3 minutes. Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
Answer:
0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 10 minutes and a standard deviation of 3 minutes
This means that [tex]\mu = 10, \sigma = 3[/tex]
Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
This is 1 subtracted by the p-value of Z when X = 15, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 10}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.
A graph of 2 functions is shown below. graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 Which of the following is a solution for f(x) = g(x)? (2 points) x = −2 x = 1 x = 0 x = −1
9514 1404 393
Answer:
(b) x = 1
Step-by-step explanation:
A graph shows the solution to f(x) = g(x) is x = 1.
__
We want to solve ...
g(x) -f(x) = 0
x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0
x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping
(x^2 -1)(x +2) +11/3(x -1) = 0 . . . . . . the difference of squares can be factored
(x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor
(x -1)(x^2 +3x +2 +11/3) = 0
The zero product rule tells us this will be true when x-1 = 0, or x = 1.
__
The discriminant of the quadratic factor is ...
b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3
This is less than zero, so any other solutions are complex.
I need all the help I can get. please assist.
4. The equation of a curve is y = (3 - 2x)^3 + 24x.
(a) Find an expression for dy/dx
5. The equation of a curve is y = 54x - (2x - 7)^3.
(a) Find dy/dx
Answer:
4(a).
Expression of dy/dx :
[tex]{ \tt{ \frac{dy}{dx} = - 2(3 - 2x) {}^{2} + 24}}[/tex]
5(a).
[tex]{ \tt{ \frac{dy}{dx} = 54 - 2(2x - 7) {}^{2} }}[/tex]
a marathon is a race that is 46,145 is a yards long. round to the nearest thousand
Answer:
46,000 yards
Step-by-step explanation:
if in the hundreds place the number is 0-499 round down
if it's 500-999 round up
two sides of a triangle measure 5 in and 12 in what could be the length of the third side
Answer:
b
Step-by-step explanation:
A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 47 states. What is the probability that she selects the route of three specific capitals?
Answer:
1 / 97290
Step-by-step explanation:
The number of ways of selecting 3 specific route capitals from 47 states can be obtained thus :
Probability = required outcome / Total possible outcomes
Total possible outcomes = 47P3
Recall :
nPr = n! / (n-r)!
47P3 = 47! / (47-3)! = 47! / 44! = 97290
Hence, probability of selecting route if 3 specific capitals is = 1 / 97290
A Food Marketing Institute found that 34% of households spend more than $125 a week on groceries. Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31
Answer:
0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population.
This means that [tex]p = 0.34, n = 124[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.34[/tex]
[tex]s = \sqrt{\frac{0.34*0.66}{124}} = 0.0425[/tex]
What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?
This is the p-value of Z when X = 0.31, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.31 - 0.34}{0.0425}[/tex]
[tex]Z = -0.705[/tex]
[tex]Z = -0.705[/tex] has a p-value of 0.2405.
0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
Can someone help me on this I can’t figure out which ones are right.
Answer:
A
Step-by-step explanation:
the function for this graph is:
[tex]y = {(x - 1)}^{2} [/tex]
so the domain (the input AKA THE x values) is all the real numbers.
find the slope of the line passing through the points (-4, -7) and (4, 3)
Answer:
5/4
Step-by-step explanation:
Use the slope formula which is y2-y1/x2-x1.
1. Plug the given values into the equation: 3-(-7)/4-(-4)=5/4
An item costs $20 and sells for $50.
a. Find the rate of markup based on cost.
b. Find the rate of markup based on selling price.
Step-by-step explanation:
50-20=30 rate of markup
4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?
Answer:
12
Step-by-step explanation:
Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202
Answer:
Kindly check explanation
Step-by-step explanation:
Rounding each number to 4 significant figures and expressing in standard notation :
(a) 102.53070,
Since the number starts with a non-zero, the 4 digits are counted from the left ;
102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2
(b) 656.980,
Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.
656.980 = 657.0 (4 significant figures) = 6.57 * 10^2
(c) 0.008543210,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3
(d) 0.000257870,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4
(e) -0.0357202,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2
