g A life insurance salesman sells on the average 3 life insurance policies per week. Calculate the probability that in a given week he will sell 2 or more policies but less 4 policies.
Answers
Answer:
44.80% probability that in a given week he will sell 2 or more policies but less than 4 policies.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
\(\mu\) is the mean in the given interval.
A life insurance salesman sells on the average 3 life insurance policies per week.
This means that \(\mu = 3\)
Calculate the probability that in a given week he will sell 2 or more policies but less 4 policies.
\(P(2 \leq X < 4) = P(X = 2) + P(X = 3)\)
In which
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
\(P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240\)
\(P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240\)
\(P(2 \leq X < 4) = P(X = 2) + P(X = 3) = 0.2240 + 0.2240 = 0.4480\)
44.80% probability that in a given week he will sell 2 or more policies but less than 4 policies.
Related Questions
Calculate the ratios in the table using the side lengths that you recorded in Part C.
Answers
Step-by-step explanation:
The ratios are;
\dfrac{BC}{AB} = \dfrac{3}{5}
AB
BC
=
5
3
\dfrac{AC}{AB} = \dfrac{4}{5}
AB
AC
=
5
4
\dfrac{BC}{AC} = \dfrac{3}{4}
AC
BC
=
4
3
\dfrac{DE}{AD} = \dfrac{3}{5}
AD
DE
=
5
3
\dfrac{AE}{AD} = \dfrac{4}{5}
AD
AE
=
5
4
\dfrac{DE}{AE} =\dfrac{3}{4}
AE
DE
=
4
3
koGiven that the lengths of the sides are;
\overline {AB}
AB
= 20
\overline {BC}
BC
= 12
\overline {AC}
AC
= 16
\overline {AD}
AD
= 10
\overline {DE}
DE
= 6
\overline {AE}
AE
= 8
The ratios are;
\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{BC}{AB} = \dfrac{12}{20} = \dfrac{3}{5}
Hypothenus
Length opposite ∠A
=
AB
BC
=
20
12
=
5
3
\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AC}{AB} = \dfrac{16}{20} = \dfrac{4}{5}
Hypothenus
Length adjacent ∠A
=
AB
AC
=
20
16
=
5
4
\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{BC}{AC} = \dfrac{12}{16} = \dfrac{3}{4}
Length adjacent ∠A
Length opposite ∠A
=
AC
BC
=
16
12
=
4
3
\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{DE}{AD} = \dfrac{6}{10} = \dfrac{3}{5}
Hypothenus
Length opposite ∠A
=
AD
DE
=
10
6
=
5
3
\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AE}{AD} = \dfrac{8}{10} = \dfrac{4}{5}
Hypothenus
Length adjacent ∠A
=
AD
AE
=
10
8
=
5
4
\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{DE}{AE} = \dfrac{6}{8} = \dfrac{3}{4}
Length adjacent ∠A
Length opposite ∠A
=
AE
DE
=
8
6
=
4
3
The group of individuals fitting a description is the _____
A.census
B.sample
C.parameter
D.population
Answers
The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.
What is population?The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.
There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.
Therefore, the correct option is D
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See full text below
A group of individuals fitting a description is the _____
Which of the term below fit the description above.
A.census
B.sample
C.parameter
D.population
Eric’s average income for the first 4 months of the year is $1,450.25, what must be his
average income for the remaining 8 months so that his average income for the year is
$1,780.75?
Answers
Answer:
$1946
Step-by-step explanation:
Eric’s average income for the first 4 months of the year is $1,450.25
Therefore, his total earning in the first four months
= 4 X $1,450.25
=$5,801
Let the average income for the remaining 8 months= x
Then:
\(\text{Eric's Yearly Average Income}=\dfrac{5801+8x}{12} \\1,780.75=\dfrac{5801+8x}{12} \\$Cross multiply\\12*1,780.75=5801+8x\\21369=5801+8x\\8x=21369-5801\\8x=15568\\Divide both sides by 8\\x=\$1946\)
Therefore, to get an average income for the year of $1,780.75, Eric must earn an average income of $1946 for the remaining 8 months.
The area of a rectangular floor is
represented by the expression
6x² + 3x - 9 feet. Which expression
could be used to express the width of the
rectangular floor?
O (x - 1) feet
(2x − 3)
feet
O (2x +9) feet
(6x + 3) feet
Answers
The expression could be used to express the width of the rectangular floor is (2x - 3) feet.
What is a rectangular floor?
A rectangular floor is a type of flooring or a floor plan that is rectangular in shape, meaning it has four sides with 90-degree angles and opposite sides that are parallel to each other.
To find the width of the rectangular floor, we need to use the formula for the area of a rectangle, which is:
Area = Length x Width
In this case, we are given the expression for the area, which is 6x² + 3x - 9. We can factor this expression to get:
6x² + 3x - 9 = 3(2x² + x - 3)
Now, we can use the fact that the area is equal to the length times the width to write:
6x² + 3x - 9 = Length x Width
We want to express the width in terms of x, so we can solve for the width by dividing both sides by the length:
Width = (6x² + 3x - 9) / Length
Width = (6x² + 3x - 9) / (3(2x² + x - 3))
Simplifying the expression, we get:
Width = (2x - 3) / (2x² + x - 3)
Therefore, the expression that could be used to express the width of the rectangular floor is (2x - 3) feet.
So the correct option is B. (2x - 3) feet.
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y=-2x +13x-2y=5how to solve the system equations algebraically?
Answers
The given equations are:
\(\begin{gathered} y=-2x+1 \\ 3x-2y=5 \end{gathered}\)So from the first equation, we have the value for y. Now we can substitute that value in the second equation for y. We have,
\(\begin{gathered} 3x-2(-2x+1)=5 \\ 3x+4x-2=5 \\ 7x=5+2 \\ 7x=7 \\ x=\frac{7}{7}=1 \end{gathered}\)Now we can substitute the value of x in the equation for y,
\(y=-2\times1+1=-2+1=-1\)Hence, x = 1 and y = -1.
You are given the following points: ????=(13,11,−20)A=(13,11,−20), ????=(−16,0,10)B=(−16,0,10), ????=(−9,16,16)C=(−9,16,16). Which point is closest to the yz-plane?
What is the distance from the yz-plane to this point? Which point is farthest from the xy-plane? ? What is the distance from the xy-plane to this point? Which point lies on the xz-plane?
Answers
a) The point which is closest to the yz-plane is B=(-16,0,10).
b) The distance from the yz-plane to this point is 16.
c) The point farthest from the xy-plane is C=(-9,16,16).
d) The distance from the xy-plane to this point 16.
e) None of the given points have a y-coordinate of 0, so there is no point that lies on the xz-plane.
a) To find the point closest to the yz-plane, we need to find the point with the smallest x-coordinate, since the yz-plane is defined by x=0. The point with the smallest x-coordinate is B=(-16,0,10), so B is closest to the yz-plane.
b) The distance from the yz-plane to point B can be found using the formula for the distance between a point and a plane, which is given by:
distance = |ax + by + cz + d| / √(a² + b² + c²)
where a, b, and c are the coefficients of the plane equation (which are 1, 0, and 0 for the yz-plane), d is the constant term (-0 in this case), and (x, y, z) are the coordinates of the point. Substituting the values for B, we get:
distance = |-16(1) + 0(0) + 10(0) + 0| / √(1² + 0² + 0²) = 16
So the distance from the yz-plane to point B is 16.
c) To find the point farthest from the xy-plane, we need to find the point with the largest z-coordinate, since the xy-plane is defined by z=0. The point with the largest z-coordinate is C=(-9,16,16), so C is farthest from the xy-plane.
d) The distance from the xy-plane to point C can be found using the same formula as before, but with the coefficients of the plane equation being 0, 0, and 1, and the constant term being 0. Substituting the values for C, we get:
distance = |0(0) + 0(0) + 1(16) + 0| / √(0² + 0² + 1²) = 16
So the distance from the xy-plane to point C is 16.
e) To find the point that lies on the xz-plane, we need to find the point with y-coordinate 0, since the xz-plane is defined by y=0. None of the given points have a y-coordinate of 0, so there is no point that lies on the xz-plane.
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Use the two given functions to write y as a function of x.
y = -3a + 3, a = -5x + 1
Answers
Answer:
Step-by-step explanation:
To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.
Given:
y = -3a + 3
a = -5x + 1
Substituting the value of "a" in the first equation:
y = -3(-5x + 1) + 3
Now, let's simplify this expression:
y = 15x - 3 + 3
y = 15x
Therefore, y can be expressed as a function of x as:
y = 15x
stu's teacher wrote his test score as a fraction. He wrote 7/10. What is his score as a percent
Answers
Answer:
that would be a seventy (70)
Answer:
70%
Step-by-step explanation:
$5,200 at 3% for 7 yearswhat is the total amount?what is the compounded interest?
Answers
p = 5200
r = 3%
t = 7 years
on a larger map the coordinates for the location of another Washington DC landmark are eight and -10 in which quadrant of the map in this landmark located explain
Answers
The other Washington DC landmark with coordinates (8,-10) is located in the fourth quadrant of the map.
To determine in which quadrant of the map a point with coordinates (8,-10) is located, we need to look at the signs of the x and y coordinates.
Since the x-coordinate (8) is positive and the y-coordinate (-10) is negative, this point is located in the fourth quadrant.
In general, the four quadrants of a Cartesian coordinate system are divided by the x and y-axes.
The first quadrant is located in the upper right-hand corner and contains points with positive x and y coordinates.
The second quadrant is located in the upper left-hand corner and contains points with negative x and positive y coordinates.
The third quadrant is located in the lower left-hand corner and contains points with negative x and y coordinates.
Finally, the fourth quadrant is located in the lower right-hand corner and contains points with positive x and negative y coordinates.
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Juan is paid a salary of $2400 biweekly. Find the Juan's earnings per year.
Answers
Answer:
2,400x26=62,400
Step-by-step explanation:
you times it by 26 because he gets paid biweekly
PLEASE HELP I NEED HELP WITH AN ALGEBRA 2 QUESTION ILL GIVE BRAINLEST
Answers
Answer:
the zeros of the function are those that result, when plugged into the equation, in zero; the zeros are -3, 1, and 1/2
Step-by-step explanation:
all possible factors:
±3/2, ±1/2, ±3, ±1
2x³ + 3x² - 8x + 3
let '2' = p and let '3' = q
factors of 'p' are 1 and 2
let '3' = q
factors of 'q' are 1 and 3
possible factors are q/p
what is the multiplicative inverse of
3/5 - 4/27 + 5/18 is it okay if i solve the equation and then the final answer i get i write multiplicative inverse of it as the final answer ..
Answers
Answer:
\(\frac{270}{197}\)
Step-by-step explanation:
First I need a common denominator. That number is 270
The volume inside a rectangular storage room is 2,070 cubic feet. The room is 3 feet high. Find the area of the floor.
Answers
Answer:
690 square ft
Step-by-step explanation:
2,070 cubic ft ÷ 3 ft = 690 ft squared
Help me asap pls i need it quick
Answers
Answer: 0.5km per hour
Step-by-step explanation:
Determine the mean, median, mode and midrange for the following data:
13 15 18 18 21
Your answers should be exact numerical values.
The mean of the data is
The median of the data is
The mode of the data is
The midrange of the data is
Answers
The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.
The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.
Let's see how to calculate Mean, Median, Mode and Midrange.
Mean = 13 + 15 + 18 + 18 + 21 / 5
Mean = 85 / 5
Mean = 17
Median = 18 (as it is the middle term of the data)
Mode = 18 (as it is most recurring number)
Midrange = 21 + 13 / 2
Midrange = 34 / 2
Midrange = 17
Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.
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Which value in the set of values below is NOT a solution to the inequality 10- 2y ≥ 4?
Set: {1, 2, 3, 4}
1. 1
2. 2
3. 3
4. 4
Answers
Answer:
Option 4: 4 is the correct answer
Step-by-step explanation:
The given inequality is:
10- 2y ≥ 4
In order to check which value is not the solution to the inequality we have to put each value in the inequality. If the inequality is true for the value, it is the solution and it is not true then it is not the solution.
Putting y = 1
\(10-2y\geq 4\\10-2(1)\geq 4\\10-2\geq 4\\8\geq 4\)
TRUE
Putting y=2
\(10-2y\geq 4\\10-2(2)\geq 4\\10-4\geq 4\\6\geq 4\)
TRUE
Putting y=3
\(10-2y\geq 4\\10-2(3)\geq 4\\10-6\geq 4\\4\geq 4\)
TRUE
Putting y=4
\(10-2y\geq 4\\10-2(4)\geq 4\\10-8\geq 4\\2\geq 4\)
FALSE
The inequality is not true for y=4.
Hence,
Option 4: 4 is the correct answer
Which diagram shows an angle bisector
Answers
B
if it is not correct sory
Diagram B is a proper demonstration of an angle bisector.
Letter A is wrong because they are a set of intersecting ines.
Letter C is wrong because they are a set of parallel lines.
Letter D is wrong because they are also a set of perpendicular lines.
So, now, we know that Letter B is the correct answer. The reason for this is also because ∠ACD is bisected by line B.
I hope that this helped answer your question. Have a good day!
Solve these with work shown please.
Answers
Step-by-step explanation:
substitute the value in the value of x and u will get the result.
Given m∠ABC=37°m∠ABC=37°and m∠CBD=165°m∠CBD=165°. According to the Angle Addition Postulate, what is the measure of ∠ABD∠ABD, that contains −−→BCBC→?
Answers
According to the Angle Addition Postulate, the measure of m∠ABD = 202°.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
The angle measures:
m∠ABC=37°,
and m∠CBD= 165°.
So, according to the angle addition postulate;
m∠ABD = m∠ABC + m∠CBD
Substituting the values,
m∠ABD = 37° + 165°
m∠ABD = 202°
Therefore, the angle measure of m∠ABD = 202°.
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Marcus made a sail for his toy boat. If the sail is 5 inches long and the top angle of the sail is 40°, what is the width of the bottom of the sail (w) to the nearest tenths place?
Answers
Answer:
4.2 in
Step-by-step explanation:
let us first visualize the sail as a triangular shape
the angle of the triangle from top is 40°
the height of the triangle is give as 5 in
we can apply SOH CAH TOA to solve for the base of the sail
the opposite = the base of the sail
the adjacent = the height of the sail= 5 in
therefore
Tan∅= Opp/Adj
Tan(40)= Opp/5
Opp= Tan(40)*5
Opp= 0.8390*5
Opp= 4.195 in
Hence the width of the sail is 4.2 in to the nearest tenths
Answer:
4.2
Step-by-step explanation:
A machine covers 5/8 sq ft in 1/4 of an hour, how much does it cover per hour?
Answers
Answer: 20/8 or 2 1/2
Step-by-step explanation:
1/4 + 1/4 + 1/4 + 1/4 = 1
5/8 + 5/8 + 5/8 + 5/8 = 2 1/2
Hope this helps!
6 cm
M
x cm
O
4 cm
x cm
B
G
The area of rectangle ABCD is 28 cm²
a) What is the length of side AB in terms of x?
length of AB =
b) If the area of rectangle ABCD is 28 cm²,
we can show that x² + ax=b where
a and b are integer values.
Work out the values of a and b.
a=
46%
(1) b=
Total marks: 3
Answers
Answer:
Step-by-step explanation:
The length of AB is (x + 4) cm and the values of a and be are a = 10, b = 4
A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other. The area of a rectangle is:
Area = length * width
From the image:
Length of AB = x + 4
Length of BC = x + 6
The area of rectangle ABCD = Length of AB * Length of BC
28 = (x + 4)(x + 6)
x² + 10x + 24 = 28
x² + 10x = 4
Comparing with x² + ax = b gives:
a = 10, b = 4
Therefore the length of AB is (x + 4) cm and the values of a and be are a = 10, b = 4
Please i need to find the era bounded by the following curves
Answers
Answer:
10 2/3 or 32/ 3
Step-by-step explanation:
5 - x^2 - (2 - 2x) =
= -x^2 + 2x + 3
Integral of (-x^2 + 2x + 3)dx from -1 to 3 =
= -x^3/3 + 2x^2/2 + 3x from -1 to 3
= -x^3/3 + x^2 + 3x from -1 to 3
= -27/3 + 9 + 9 - (1/3 + 1 - 3)
= -9 + 9 + 9 - 1/3 - 1 + 3
= 11 - 1/3
= 10 2/3 = 32/3
Answer:
32/3
Step-by-step explanation:
Check the pdf :)
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
Answers
The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.
The graph is given in the question.
As per the given line, we take two points (0, 4) and (5, 8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 4
x₂ = 5, y₂ = 8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 4 = (8 - 4)/(5-0 )[x -0]
⇒ y - 4 = (4/5)x
⇒ y = (4/5)x + 4
The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.
So, the equation of the line would be y = (4/5)x + 4.
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The Fairplay sporting goods store sells two
different models of a popular fitness tracker. In
a month the store sold 42 trackers for a total of
$6,574. Write and solve a system of equations
that can be used to determine the number of
each unit sold.
Answers
The final statement is The linear equation is xx₁+xy₁=6532
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: Total trackers sold =42 and total sales=$6574
let x models of 1st model and 42-x models of 2nd model be sold and their respective selling price be x₁ and y₁, then we have
xx₁+42+xy₁=6574
xx₁+xy₁=6532
Hence, The linear equation is xx₁+xy₁=6532
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Which represents the solution of the graphed system of equations, y=x^2-2x and y=-2x-1
Answers
Answer:
x = √(-1) = i
Since the value of √(-1) is not real.
The system has no real solution.
Step-by-step explanation:
The solution to the system of equations is at the point where they intercept each other.
y1 = y2
For the given equation;
y=x^2-2x and y=-2x-1
To get the where they intercept, we will equal both equations;
y=x^2-2x = -2x-1
x^2 - 2x = -2x - 1
x^2 - 2x + 2x + 1 =0
x^2 +1 = 0
x^2 = -1
x = √(-1) = i
Since the value of √(-1) is not real.
The system has no real solution.
739000 : 1000
What’s the answer ???
Answers
Here it is
739000/1000 = 739
93/100
Natalie needs 3 1/2 cups of flour to make 4 dozen cookies. How many.cups will she
need to make 2 dozen cookies?
7 cups
1 cup
13/4 cups
11/2 cups
Answers
Answer:
3/4 cups
Step-by-step explanation:
3 1/2 divided by 2
Find the least common multiple and greatest common factor of 10,8
Answers
Explanation:
10/2 = 5
8/2 = 4
5 and 4 don’t have a common factor