Using the Poisson distribution, the probabilities are given as follows:
A. 0.0888 = 8.88%.
B. 0.1354 = 13.54%.
C. 0.8646 = 86.46%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.Item a:
10 hours, 2 calls per hour, hence the mean is given by:
[tex]\mu = 2 \times 10 = 20[/tex].
The probability is P(X = 20), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 20) = \frac{e^{-20}20^{20}}{(20)!} = 0.0888[/tex]
Item b:
1 hour, hence the mean is given by:
[tex]\mu = 2[/tex]
The probability is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1354[/tex]
Item c:
The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1354 = 0.8646[/tex]
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Transportation officials tell us that 60% of drivers wear seat belts while driving. Find the probability that more than 562 drivers in a sample of 900 drivers wear seat belts.
The probability that more than 562 drivers is 0.9328
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given: p = 0.60
n = 900
Let X denote the number of drivers that wear a seat belt,
P(X > 562)
[tex]\mu[/tex] = n*p = 900(0.60) = 540
[tex]\sigma^{2}[/tex]= n*p*(1-p)
=900*0.60*0.40
=216
P(X >562) = Pr( Z > 1.4976)
= 0.9328
Hence, the probability that more than 562 drivers is 0.9328
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Identifying Proportional Relationships
Which graph represents a proportional relationship?
Answer:
I can't answer this if you don't have the answer choices
I'm sorry
If you drive 72 miles and use 6 gallons of gas, what is your rate
Answer:
Well, it depends if you are asking the rate per gallon it would be 12 miles per gallon.
The credit remaining on a phone card (in dollors) is a linear function of the total calling trime made with the card ( in minutes). The remaining credit after 22 minutes is $36.70, and the remaining credit after 52 mintues is $32.20. What is the remaining credit after 85 mintues of calls?
After 85 minutes of calls, there are $27.25 left on the card.
What is the remaining credit after 85 minutes of calls?
A linear equation in slope-intercept form is:
y = a*x + b
Where a is the slope.
If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)
(points of the form (time, dollars)).
So the slope is:
[tex]a = \frac{32.2 - 36.7}{52 -22} = -0.15[/tex]
The linear equation is then:
y = -0.15*x + b
To find the value of b, we use the point (22. 36.7)
36.7 = -0.15*22 + b
36.7 + 0.15*22 = b = 40
Then the linear equation is:
y = -0.15*x +40
The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.
y = -0.15*85 + 40 = 27.25
This means that after 85 minutes of calls, there are $27.25 left on the card.
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If you could please answer this that would be awesome!
Please graph it!
The graph is attached with the answer, This is looking like a horizontal staircase
What is a Step Function ?A step function is a piece wise function whose all pieces are horizontal line or a point.
It is given in the question to graph the interval
-2 ≤x≤2
for f(x) = |x+3|
-2 1
-1 2
0 3
1 4
2 5
The graph is attached with the answer.
This is looking like a horizontal staircase
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What is the value of h?
Answer:
h=-2
Step-by-step explanation:
the graph was shifted 2 units left
(
Given that a = 7 cm and b = 8 cm,
work out the area of the triangle.
Give your answer rounded to 1 DP.
a
cm²
b
The diagram is not drawn accurately.
Answer:
28cm²
Step-by-step explanation:
The area of a triangle is given as:
= 1/2 × b × h
= 1/2 × 7 × 8
= 28cm²
What negative Z-score (standard score) would the area under the curve be 0.8621
z* = _______
Factor the polynomial function.
G(v) - 196v² + 100
Answer:
4(49v²+25)
Step-by-step explanation:
[tex]196 {v}^{2} + 100[/tex]
[tex]4(49 {v}^{2} + 25)[/tex]
How much of an alloy that is 30% copper should be mixed with 200 ounce of an alloy that is 70% copper in order to get an alloy that is 40% copper?
The alloy of copper will be 600 ounces.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Let us represent
Number of ounce of 30% copper = x
Hence, our Equation will be given below:-
x × 30% + 200 × 70% = (x + 200) × 40%
0.3x + 140 = (x + 200)0.4
0.3x + 140 = 0.4x + 80
Collect like terms
0.4x - 0.3x = 140 - 80
0.1x = 60
x = 60/0.1
x = 600 ounces
Therefore the alloy of copper will be 600 ounces.
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. . . , , ,
help please
The system of inequalities of the graph is (a) y > x² + 2x - 3 and y > 2x + 3
How to determine the inequalities?The complete question requires that we determine the system of inequalities of the graph (the graph is attached)
Going by the list of options, the equation of the quadratic curve is:
y = x² + 2x - 3
From the graph, we can see that:
The curve uses a dotted lineThe upper part is shadedThe above means that the inequality is greater than i.e. >
So, we have:
y > x² + 2x - 3
The above eliminates options (b) and (c)
From the graph, we can see that the straight line has a positive slope, a dotted line and the upper part is shaded.
The linear inequality in option (a) has the above characteristics.
So, the inequality is:
y > 2x + 3
Hence, the system of inequalities of the graph is (a) y > x² + 2x - 3 and y > 2x + 3
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Assume that t varies jointly as r and q2². If t=320 when r=5 and q = 4, what is the value of q when r= 1 and t= 196?
q=
Step-by-step explanation:
[tex]t = k(r)( {q}^{2} )[/tex]
[tex]320 = k(5)( {4}^{2} )[/tex]
[tex]320 = 80k[/tex]
[tex]k = 4[/tex]
[tex]196 = 4(1)( {q}^{2} )[/tex]
[tex]49 = {q}^{2} [/tex]
[tex]q = 7[/tex]
What amount would u have if u deposited 1800 a year for 30 years at 7% compounded annually
Answer: $183,731
Step-by-step explanation:
After 30 years, the interest is $183,731
Find the radius of a circle with area 345 square centimetres
30 pts need in like 10 mins!!
Please say the answer like-
… divided by … = ……
Or
… times … = …..
Answer:
5.9
Step-by-step explanation:
It's because area is 345
Formula , A=πr2Find the √ of 34518.6=3.14×f2fR = 5.9Statement: "Three less than four times a number is greater
than or equal to 41."
Answer:
x≥11
Step-by-step explanation:
4x-3≥41
4x≥41+3 -44
x≥44/4 = 11
the amount of money sue needs to pay (m) equals $30 to go to an apple orchard and pick apples plus $5 for every bushel of apples (b) she takes home
the elegante is aborto 3
There is a 45% chance of snow on Friday. Thereis a 78% chance that I will go sledding if it snows. What is the probability that I will go
sledding?
Answer:
35.1% chance of going sledding
Step-by-step explanation:
45% chance of snow on Friday
Convert percentage to decimal form (divide by 100)
45% = 0.45
78% chance of sledding if it snows
Convert percentage to decimal form (divide by 100) to multiply
78% = 0.78
Multiply to find the probability of both occurring
0.78 * 0.45 = 0.351
Convert back into a percentage (multiply by 100)
0.351 = 35.1% chance of sledding
Let me know if you have any questions!
Solve for x in the equation 4/x-3=x
Answer:
jenejebdjdndnr
r
r
r
r
r
r
Answer:
Step-by-step explanation:
Comment
Multiply through by x - 3
Then factor the result
4*(x - 3) / (x - 3) = x*(x - 3)
4 = x * (x - 3 ) Remove the brackets
4 = x^2 - 3x Subtract 4 from both sides
4-4 = x^2 - 3x - 4 Simplify
0 = x^2 - 3x- 4
This factors
0=(x - 4)(x + 1)
Answer
x - 4 = 0
x = 4
x+ 1 = 0
x = - 1
What are the zeros of the quadratic function f(x)=6x^2+12x-7
Answer:
[tex]A) \ x=-1 \ ^ +_-\frac{\sqrt{13} }{\sqrt{6}}.[/tex]
Step-by-step explanation:
if to solve the given equation, then
D=6²+42=78;
[tex]\left[\begin{array}{ccc}x=\frac{-6-\sqrt{78}}{6} \\x=\frac{-6+\sqrt{78}}{6} \end{array} \ = > \ \left[\begin{array}{ccc}x=-1-\sqrt{\frac{13}{6} } \\x=-1+\sqrt{\frac{13}{6} } \end{array}[/tex]
Question 3(Multiple Choice Worth 4 points)
Which expression is equivalent to 73.7-57
0 72
0 77
17
글
Answer: [tex]\frac{1}{7^{2}}[/tex]
Step-by-step explanation:
Using the exponent rule [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex], we get that
[tex]7^{3} \cdot 7^{-5}=7^{-2}[/tex]
Then, using the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex], we get that
[tex]7^{-2}=\boxed{\frac{1}{7^{2}}}[/tex]
A water tank in the shape of an inverted circular cone has a base radius of 3 m and height of 7 m . If water is being pumped into the tank at a rate of 4.3 m^3 / min , find the rate at which the water level is rising when the water is 3.5 m deep. (Round your answer to three decimal places if required)
The water level increases by 0.608 meters per minute when the water is 3.5 m deep
How to determine the rate?The given parameters are:
Radius, r = 3Height, h = 7Rate in, V' = 4.3m^3/minThe relationship between the radius and height is:
r/h = 3/7
Make r the subject
r = 3h/7
The volume of a cone is;
[tex]V = \frac 13\pi r^2h[/tex]
This gives
[tex]V = \frac 13\pi (\frac{3h}{7})^2h[/tex]
Expand
[tex]V = \frac{3h^3}{49}\pi[/tex]
Differentiate
[tex]V' = \frac{9h^2}{49}\pi h'[/tex]
Make h' the subject
[tex]h' = \frac{49}{9\pi h^2}V'[/tex]
When the water level is 3.5.
We have:
[tex]h' = \frac{49}{9\pi * 3.5^2}V'[/tex]
Also, we have:
V' = 4.3
So, the equation becomes
[tex]h' = \frac{49}{9\pi * 3.5^2} * 4.3[/tex]
Evaluate the products
[tex]h' = \frac{210.7}{346.36}[/tex]
Evaluate the quotient
h' = 0.608
Hence, the water level increases by 0.608 meters per minute
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Which table correctly shows all the sample spaces for tossing a coin to get heads and rolling a number on a six-sided number cube?
Using it's concept, the sample space for the experiment is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
What is the sample space of an experiment?The sample space is the set that contains all possible outcomes for an experiment.
In this problem:
For the coin, there are 2 outcomes, H for heads and T for tails.For the number, there are 6 outcomes, which are the 6 numbers.Hence the sample space is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
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Want to earn 20 points for correct answer CLICK ME
Answer:
64 is the answer
Step-by-step explanation:
Mark me brainliest answer pls
Find the inverse of the function y = 3x + 5 Find the inverse of the function y=3x+5
Answer:
First Inverse function= f^-1(x)=x/3-5/3
Second Inverse function=f^-1(x)=x/3-5/3
Step-by-step explanation:
Your load is a container full of water. The container measures
1.0m x 1.25m x 1.1m and weighs 50kg when empty. Since 1 cubic
metre of water weighs 1 tonne, find the weight of the load
Answer:
1282kg
Step-by-step explanation:
1.0*1.12*1.1=1.232 tonnes
50kg + 1232kg = 1282kg
Hope this helps :)
The number of measles cases increased 36.5% to 193 cases this year. What was the number of cases prior to the increase? The number of measles cases increased 36.5 % to 193 cases this year . What was the number of cases prior to the increase ?
Answer:
70.445
Step-by-step explanation:
you have to subtract 36.5 by 193.
Look at the photo and answer it pls
Answer:
There isn't a photo
Step-by-step explanation:
There is no photo
Answer this please, thank you in advance :D
i) Student A used the property of the power of a power and student B used the definition of power and the property of the product of power with the same base. ii) Both were correct.
How to understand power properties
In this question we must analyze the procedure used by each student to simplify a power into the form rⁿ:
i) The student A used the property of the power of a power which states that [tex](r^{m})^{n} = r^{m\cdot n}[/tex]. In exchange, the student B used the definition of power and the property of the product of powers with the same base.
ii) Based on the description in i), both students used correct methods of simplifying.
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Leah wants to buy a home for
$380,000, but can only get a loan from the bank for $330,600. What percentage does Leah have to put down in order to pay for the home?
Leah have to put down 13% of the total money in order to pay for the home.
What is a Home Loan ?The amount of money a person borrows from a bank to buy a house is termed as Home Loan.
It is given that
Leah wants to buy a home for $380,000
The amount of money he can get from bank is $ 330,600
The amount of money Leah needs to have
= $ 380000 - $ 330600 = $49400
The percentage Leah have to put down in order to pay for the home is
=($49400 /$380000 ) * 100%
= 0.13 * 100 %
= 13%
Therefore Leah have to put down 13% of the total money in order to pay for the home.
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If I=$312.50 R=25% T=0.25 what is P
Step-by-step explanation:
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