Answers
Therefore, the expected value of the event P(2k) for 2 ≤ k ≤ 6, given the event E, is 96/1 or simply 96.
What is probability?Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.
Here,
We can start by calculating the probability of each event in the sample space:
P(1) = 1/32
P(4) = 1/8
P(8) = 1/4
P(16) = 1/2
P(32) = 1
P(64) = 1
Next, we can calculate the probability of the event E by summing the probabilities of the individual outcomes in E:
P(E) = P(1) + P(8) + P(32) + P(64)
= 1/32 + 1/4 + 1 + 1
= 33/32
Now, we can calculate the expected value of the event P(2k) for 2 ≤ k ≤ 6:
E[P(2k)] = Σ[2 ≤ k ≤ 6] P(2k) * ΘS(2k)
= P(4)*ΘS(4) + P(8)*ΘS(8) + P(16)*ΘS(16) + P(32)*ΘS(32) + P(64)*ΘS(64)
= (1/8)*4 + (1/4)*8 + (1/2)*16 + (1)*32 + (1)*64
= 4/8 + 8/4 + 16/2 + 32 + 64
= 1/2 + 2 + 8 + 32 + 64
= 106.5
Therefore, the expected value of the event P(2k) for 2 ≤ k ≤ 6, given the event E, is 106.5. However, since the event E has a probability greater than 1, this result does not make sense. So, we need to normalize the probabilities of the events by dividing them by P(E) to obtain the correct expected value:
P'(1) = P(1)/P(E) = (1/32)/(33/32) = 1/33
P'(8) = P(8)/P(E) = (1/4)/(33/32) = 8/33
P'(32) = P(32)/P(E) = 1/(33/32) = 32/33
P'(64) = P(64)/P(E) = 1/(33/32) = 32/33
Now, we can calculate the normalized expected value:
E[P(2k)] = Σ[2 ≤ k ≤ 6] P'(2k) * ΘS(2k)
= P'(8)*ΘS(8) + P'(32)*ΘS(32) + P'(64)*ΘS(64)
=(8/33)*8 + (32/33)*32 + (32/33)*64
= (64/33) + (1024/33) + (2048/33)
= 3136/33
= 96/1
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Related Questions
Please help me I don’t understand this
Answers
Answer:
the required answer are -8,0,4
Find the angles of △ABC given that a=11, b=20, and c=18.
Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles.
Answers
The angles of △ABC are approximately:
A ≈ 36.1 degrees
B ≈ 55.9 degrees
C ≈ 101.3 degrees
Angles of triangle calculation.
To find the angles of △ABC, we can use the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
where C is the angle opposite the side c.
Using the given values, we can substitute and solve for cos(C):
18^2 = 11^2 + 20^2 - 2(11)(20)cos(C)
324 = 441 + 400 - 440cos(C)
cos(C) = -17/440
C ≈ 101.3 degrees
We can now use the Law of Sines to find the other angles:
sin(A)/a = sin(C)/c
sin(A)/11 = sin(101.3)/18
sin(A) ≈ 0.593
A ≈ 36.1 degrees
sin(B)/b = sin(C)/c
sin(B)/20 = sin(101.3)/18
sin(B) ≈ 0.820
B ≈ 55.9 degrees
Therefore, the angles of △ABC are approximately:
A ≈ 36.1 degrees
B ≈ 55.9 degrees
C ≈ 101.3 degrees
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can someone please help me ASAP
please show your work on paper
Wrong Answers Will Be Reported !
Answers
The expressions are solved to give;
1.n = 1
2. h = 1
3. x = -5
4. n = 1/4
5. x = 7/2
6. p = 2/3
7. x = -12
8. n = 3
9. c = -1
10. x = 6
What are algebraic expressions?These are expressions that are made up of term, variables, constants, factors and coefficients.
They are also made up of mathematical operations.
From the information given, we have;
1. 5n + n = 2n + 4
collect and add the like terms
4n = 4
Make n subject
n = 1
2. 5h + 2 = h - 2
collect and add the like terms
4h = 4
h = 1
3. 2x - 1 = 3x + 4
collect and add or subtract the like terms
-x = 5
x = -5
4. n = n + 1/5
cross multiply
4n = 1, n = 1/4
5. x + 5 = 3x - 2
collect like terms
-2x = -7
x = 7/2
6. p = p + 2/4
cross multiply
3p = 2
p = 2/3
7. 4(2 + x) = 3x - 4
expand the bracket
8 + 4x = 3x - 4
collect like term
x = -12
8. 5n + 2 = 3n + 4
collect like terms
n = 3
9. 3c - 2 = -3c - 8
collect like terms
6c = - 6
c = -1
10. 3x + 1 = 2x - 5
collect the like terms
x = 6
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3. Gabe has $100. He plans to buy a jersey for $55. He will spend the rest of his money on T-shirts, which cost $15 each. Which inequality could Gabe use to find s, the number of T-shirts he can buy?
A 55 + 15s ≤ 100
B 15 + 55s ≤ 100
C 55 + 15s ≤ 100
D 15 + 55s ≤ 100
Answers
Find cos (A) I need help with this question
Answers
Answer:
[tex]\frac{8}{10}[/tex]
Step-by-step explanation:
[tex]cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}[/tex]
Answer:
Answer:
\frac{8}{10}
10
8
Step-by-step explanation:
\begin{gathered}cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}\end{gathered}
cos(A)=
hypotenuse
adjacent
=
AC
AB
=
10
8
if necessary.
21. A company makes specialized fish tanks, like the one shown below. If 1 gallon = 0.134 ft³, how many
gallons of water will it take to fill the fish tank completely?
9 ft
2 ft
3 ft
V = 6
Answers
It would take about 402.985 gallons of water to fill the fish tank completely.
What is the amount of water?To calculate the number of gallons of water it would take to fill the fish tank completely, we need to multiply the dimensions of the fish tank in cubic feet by the conversion factor to convert cubic feet to gallons.
Given:
Length = 9 ft
Width = 2 ft
Height = 3 ft
Conversion factor: 1 gallon = 0.134 ft³
Step 1: Calculate the volume of the fish tank in cubic feet
Volume = Length × Width × Height = 9 ft × 2 ft × 3 ft = 54 ft³
Step 2: Convert cubic feet to gallons
54 ft³ × (1 gallon / 0.134 ft³) ≈ 402.985 gallons
So, it would take approximately 402.985 gallons of water to fill the fish tank completely.
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The committee members will spend money to rent the following equipment:
• 2 fog machines
• 1 sound equipment set-up
• 1 disco ball
They already spent $855 on lighting and $462 on costumes.
Each audience member will receive a gift that costs $1.15 each.
What is the total amount of money, in dollars, the committee will spend on the talent show?
Item
Spotlight
Fog machine
Sound equipment set-up
Disco ball
Cost Per Item
$ 45 each
$ 40 each
$165 each
$ 45 each
Answers
Answer:
1,607 plus the amount of people multipled by 1.15
Step-by-step explanation:
2 fog machines = $80
1 sound equipment = $165
1 disco ball = $45
80+165+45+855+462= $1,607
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
ASA
SAS
AAS
None
Answers
The method you would use to prove the two triangles are congruent include the following: B. ASA.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
you did not provide enough information to answer the question
Find the indicated functional value for the ceiling function: f(−0.75)?
A. -1
B. 1
C. 2
D. 0
Answers
The ceiling function, denoted by ⌈x⌉, gives the smallest integer that is greater than or equal to x. Therefore, ⌈-0.75⌉ is the smallest integer that is greater than or equal to -0.75.
Since -1 is the smallest integer that is greater than or equal to -0.75, we have:
⌈-0.75⌉ = -1
Therefore, the functional value for the ceiling function at -0.75 is -1.
The answer is option A.
Kendra invests $5800 in an account that earns 5.2% annual interest compounded quarterlyHow much will be in the account after 5 years? Round to the nearest cent.
Answers
Answer:
30508
Step-by-step explanation:
5800(1+0.052)^5
Course Activity: Pythagorean Triples
Question
Determine if each set of numbers can be the lengths of the sides of a right triangle.
Select the correct text in the table.
(
52
b
12 13
12 35
5
10
8
12
20
99
Pythagorean triple?
Yes No
2013 Yes No
5√5 Yes No
15 Yes No
101 Yes No
Answers
the correct response to the question is: Yes, No, Yes, No and Yes.
How to determine if set of numbers can be the lengths of the sides of a right triangle?We can determine if each set of numbers can be the lengths of the sides of a right triangle by evaluating each set.
Evaluating each set :
#1 :
5, 12, 13
5² + 12² = 13²
25 + 144 = 169
169 = 169
It is a Yes
#2 :
12, 35, 20
12² + 35² = (20√3)²
144 + 1225 = 400*3
1369 ≠ 1200
It is a No
#3 :
5, 10, 5√5
5² + 10² = (5√5)²
25 + 100 = 25(5)
125 = 125
It is a Yes
#4 :
8, 12, 15
8² + 12² = 15²
64 + 144 = 225
208 ≠ 225
It is a No
#5 :
20, 99, 101
20² + 99² = 101²
400 + 9801 = 10201
10201 = 10201
It is a Yes
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The question lacks some details, see complete question in the attached image.
Match the orange graph above to the corresponding equation.
Answers
The equation for the orange graph is the one in the last option:
f(x) = -3x³
Which is the equation for the orange graph?We can see that the orange graph seems to be:
A cubic function.It has a negative leading coefficient, because when x > 0 the graph goes downwards.The graph is narrower than the parent cubic function, then the leading coefficient is larger than 1.From the given options, the only one that matches all these options is the last one:
f(x) = -3x³
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help this is due today!!!
Answers
Answer:
46
Step-by-step explanation:
46 (ve had this problem before)
A bike shop has 11 red bikes, 3 blue bikes, 4 orange bikes, and 12 sliver bikes
Answers
Answer:
It Does. Cool
Answer:
c.) silver bikes
Step-by-step explanation:
Given the bike shop has 11 red bikes, 3 blue bikes, 12 silver bikes
here, the number orange bikes = 4
Given for every 1 orange bike there 3 __ bikes
Divide each number of bikes by the number of orange bikes
For 11 red bikes
= 11/4 = 2.75 [which means for 1 orange bike 2.75 red bikes ]
For 3 blue bikes
= 3/4 = 0.75 [ which means for 1 orange bike 0.75 blue bikes ]
For 12 silver bikes
= 12/4 = 3 [ which means for 1 orange bike 3 silver bikes ]
For every 1 orange bike, there are 3 silver bikes.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday
49 55 42 46 47 42 38
Julia measured the high temperature in her town for one week. Using the chart above, find the mean absolute deviation for the high temperatures. Round your answer to the nearest tenth.
Be sure to show your work for finding:
the mean of the set of data
the distance of each number from the mean
the mean absolute deviation
Answers
the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.
How to solve the question?
To find the mean absolute deviation (MAD) for the high temperatures in Julia's town, we first need to find the mean temperature for the week.
To do this, we add up all the temperatures and divide by the number of temperatures:
(49 + 55 + 42 + 46 + 47 + 42 + 38) ÷ 7 = 43.3
The mean temperature for the week is 43.3 degrees.
Next, we need to find the distance of each temperature from the mean. To do this, we subtract the mean from each temperature:
|49 - 43.3| = 5.7
|55 - 43.3| = 11.7
|42 - 43.3| = 1.3
|46 - 43.3| = 2.7
|47 - 43.3| = 3.7
|42 - 43.3| = 1.3
|38 - 43.3| = 5.3
We take the absolute value of each difference to ensure that the distances are positive.
Now, we find the mean of the distances by adding up all the distances and dividing by the number of temperatures:
(5.7 + 11.7 + 1.3 + 2.7 + 3.7 + 1.3 + 5.3) ÷ 7 = 4.9
Therefore, the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.
In conclusion, the mean absolute deviation is a measure of the variability of a set of data. It is calculated by finding the mean of the absolute distances of each data point from the mean. In this case, the MAD is 4.9 degrees, indicating that the temperatures for the week were relatively close to the mean.
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EASY ALGEBRA 2 !! PLEASE HELP
Answers
according to the question the balance in the account earning compound interest after 6 years is $4,156.22.
what is interest ?Multiply the principal with the rate of interest, the time period, and various other factors to determine simple interest. Simple returns = money + interests + hours is the marketing formula. This approach makes calculating interest the simplest. The approach to calculating interest that is most usually employed is as a percentage over the principal sum. For instance, he will just pay his share of the interest at 100% when he borrows $100 with a friend and agrees to shell out it back with 5% interest. $100 has been reduced to $5 (0.05). Every time you borrow money, you must pay interest, which is applied to whatever loans you make. On the loan balance, interest is typically calculated using an annual percentage.
given,
To calculate the balance in the account earning compound interest after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the sum of money at the end of the period of time
P stands for the principle (beginning sum).
the decimal representation of the annual interest rate (r).
n represents how many times the interest rate is compounded annually.
t is the duration (in years).
In this case, we have:
P = $3500 (the principal)
r = 2.16% = 0.0216 (the annual interest rate)
Since interest is compounded four times a year (quarterly), n is equal to four.
t = 6 (the time period is 6 years)
With these values entered into the equation, we obtain:
A = 3500(1 + 0.0216/4)^(4*6)
A = $4,156.22
Therefore, the balance in the account earning compound interest after 6 years is $4,156.22.
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The balance in the account earning compound interest after 6 years when the principal is $3500 at an annual interest rate of 2.16% compounded quarterly is approximately $4,029.53.
What is compound interest?Compound interest is the term used to describe the interest that is calculated on both the initial investment and any accumulated interest. It is interest on top of interest, to put it another way.
We can use the formula for compound interest to find the balance in the account after 6 years:
A = P(1 + r/n)^(nt)
where:
A = balance after 6 years
P = principal = $3500
r = annual interest rate = 2.16%
n = number of compounded times per year = 4 (quarterly)
t = time in years = 6
Plugging in the values, we get:
A = 3500(1 + 0.0216/4)^(4×6)
A ≈ $4,029.53
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please help me with this question..
Answers
The possible values of a are 3 and -3.
How to find the value of a?We know that the coefficient of x⁷ in the given expression is 1215, the expression is:
[tex]x^3(ax + 3)^5[/tex]
The term with x⁷ will be:
[tex]5*(3x^7*a^4) = (15a^4)*x^7[/tex]
Then we need to solve the equation:
15a⁴ = 1215
a⁴ = 1215/15
a⁴ = 81
a = ⁴√81 = ± 3
These are the possible values of a.
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Drag each number to the correct location on the table.
Complete a two-way frequency table using the given probability values.
Answers
The complete table as determined from the given probabilities is given below:
X Y Total
A 40 28 68
B 38 54 92
Total 78 82 160
What is the probability P(A|B)?P(A|X) means the conditional probability of A given X has occurred. In this case, 40/92 means out of 92 times X occurred, A occurred 40 times.
P(B) means the marginal probability of B, which is the total probability of B occurring regardless of whether A occurred or not. In this case, 78/160 means out of 160 trials, B occurred 78 times.
The row and column totals are calculated by adding up the corresponding values.
The grand total is the sum of all the values in the table.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See the attached image.
There are spiders and dogs in Veronica's backyard. Veronica sees 240 legs in total. The total number of animals (spiders and dogs) is 3 times the amount of spiders. How many spiders are in the backyard?
Answers
There are 15 spiders in the backyard. The correct option is D
To solve this problemLet's begin by resolving the issue using algebra. Let's use "s" for the quantity of spiders and "d" for the quantity of dogs in the backyard.
As a result of the difficulty, we know that there are 3 times as many animals as there are spiders.
s + d = 3s
Simplifying this equation, we get:
d = 2s
We also know that there are 240 legs in the backyard, with each dog having 4 legs and each spider having 8. Thus, we can create the following equation:
8s + 4d = 240
Substituting d = 2s, we get:
8s + 4(2s) = 240
Simplifying and solving for s, we get:
16s = 240
s = 15
Therefore, there are 15 spiders in the backyard.
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What is the slope of the line
Answers
Step-by-step explanation:
Look at the points (0,-3) and ( 3,0)
slope, m = rise / run = 3 / 3 = 1
Answer:
1
Step-by-step explanation:
y=x+3
Forty-two divided by seven plus the quantity three divided by six
Answers
Therefore , the solution of the given problem of expression comes out to be 6.5 is the abbreviated numerical expression.
What is an expression?Shifting numbers, which can be expanding, variable diminishing, or blocking, should be used instead of random estimations. Only through exchanging goods like tools, expertise, or answers to problems could they assist one another. The explanation on the reality equation may include the justifications, elements, or mathematical claims for tactics like increased argumentation, falsification, and blending.
Here,
The mathematical expression is expressed as follows:
=> 42 / 7 + (3 / 6)
We can use the division operations to make the expression simpler:
=> 7 /42 = 6
=> 6 / 3 = 0.5.
The statement is thus more easily expressed as follows:
=> 6 + 0.5
When we add the two numbers, we get:
=> 6.5
Therefore, 6.5 is the abbreviated numerical expression.
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The complete question is " Write and simplify this numerical expression. Forty-two divided by seven plus the quantity three divided by six"
Is (3, 5) a solution to this system of equations?
y = 5
Y= -5/3x+10
yes
E
Answers
Answer:
no
Step-by-step explanation:
-5/3x+10=5
-5/3x=5-10=-5
3x=-5/-5=1
=>x=1/3
Find the 61st term.
O, 6, 12, 18, 24, ...
61st term = [?
Answers
Answer: i think its 366
Step-by-step explanation:
i just did 61X6
(4+sqrt -20i)+(5+sqrt -30i)
Answers
The sum of the two complex numbers is 9 - √30) + 2√(5)i.
Explain complex numbers
Complex numbers are numbers that consist of a real part and an imaginary part, expressed as a+bi, where a and b are real numbers and i is the imaginary unit. They are used in mathematics to represent solutions to equations that cannot be solved using only real numbers.
According to the given information
To add complex numbers (4+√(-20i)) and (5+√(-30i)), we add their real parts separately and their imaginary parts separately:
Real parts: 4 + 5 = 9
Imaginary parts: √(-20i) + √(-30i)
We can simplify each of the square roots using the fact that:
√(-1) = i
Therefore:
√(-20i) = √(20) * √(i) = 2√(5) * i
√(-30i) = √(30) * √(i) = √30) * i * √(-1) = √(30) * i^2 = -√(30)
So the imaginary parts simplify to:
2√(5)i - √(30)
Putting it all together, we get:
(4+√(-20i)) + (5+√(-30i)) = 9 + (2√(5)i - √(30)) = 9 - √(30) + 2√(5)i
Therefore, the sum of the two complex numbers is 9 - √(30) + 2√(5)i.
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Find the volume of a tissue box that has the following dimensions:
Length=20 cm
Width= 5 cm
Height= 12 cm
Volume=______
Answers
Answer:
1,200
Step-by-step explanation:
The formula is Length x Width x Height so it will be 20 x 5 x 12 and you get 1,200.
Hope this helps!
V=20*5*12
V=1,200cm^3
in a survey, 1500 adults in a country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean is lower: 38.4 hours and upper 43.5. Which of the following represents a reasonable interpretation of the results
Answers
The average number of hours worked in the previous week for adults in the country is likely to be between 38.4 and 43.5 hours.
Based on the survey results of 1500 adults, we can be 95% confident that the true mean number of hours worked in the previous week for the entire population of the country lies between 38.4 hours and 43.5 hours.
This means that if we were to repeat this survey multiple times, 95% of the time the sample mean would fall within this range. Therefore, we can conclude that the average number of hours worked in the previous week for adults in the country is likely to be between 38.4 and 43.5 hours.
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Find the surface area of a pyramid (which has 4 triangular sides and 1 square base) that has triangular height of 6 feet and base length of 4 feet.
Answers
The surface area of the pyramid is 64 square feet.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To find the surface area of the pyramid, we need to find the area of each face and add them together.
First, let's find the area of the base, which is a square with side length 4 feet:
Area of base = 4 feet x 4 feet = 16 square feet
Next, we need to find the area of each triangular face. We know that the height of each triangular face is 6 feet, and the base of each triangular face is one of the sides of the square base, which is 4 feet. To find the area of a triangle, we use the formula:
Area of triangle = 1/2 x base x height
Area of each triangular face = 1/2 x 4 feet x 6 feet = 12 square feet
There are 4 triangular faces, so the total area of all the triangular faces is:
Total area of triangular faces = 4 x 12 square feet = 48 square feet
Now we can find the total surface area by adding the area of the base and the area of the triangular faces:
Total surface area = area of base + area of triangular faces
Total surface area = 16 square feet + 48 square feet
Total surface area = 64 square feet
Therefore, the surface area of the pyramid is 64 square feet.
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Find the area
Round to nearest tenth
Answers
Split the shape into a rectangle and two triangles
Area of rectangle = 7*18.5
=129.5
Area of triangles = 2(1/2(10.4*15.3)
=159.12
Total area = 159.12+129.5
= 288.62 mm^2
Rounded to the nearest tenth is 288.6
The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $75,000 10-year term policy for a 25-year-old male. Round your answer to the nearest cent. A 5-column table with 6 rows titled Term Insurance. Column 1 is labeled Age with entries 20, 21, 22, 23, 24, 25. Column 2 is labeled 5-year term male with entries 2 dollars and 43 cents, 2.49, 2.55, 2.62, 2.69, 2.77. Column 3 is labeled 5-year term female with entries 2.07, 2.15, 2.22, 2.30, 2.37, 2.45. Column 4 is labeled 10-year term male with entries 4.49, 4.57, 4.64, 4.70, 4.79, 4.85. Column 5 is labeled 10-year term female with entries 4.20, 4.36, 4.42, 4.47, 4.51. a. $363.75 c. $183.75 b. $207.75 d. $338.25
Answers
None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.
what is rounding ?
Rounding is a mathematical process of approximating a number to a specified degree of accuracy. It involves replacing a number with a simpler, but close value that is easier to work with or understand.
In the given question,
The question asks us to find the annual premium for a $75,000 10-year term policy for a 25-year-old male, using the table of annual life insurance premiums per $1,000 of face value.
First, we need to find the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. Looking at the table, we can see that the premium for a 10-year term policy for a 25-year-old male is $4.79 per $1,000 face value.
To find the annual premium for a $75,000 policy, we need to multiply the premium per $1,000 face value by 75. So:
Annual premium = $4.79 per $1,000 x 75 = $359.25
Rounding this answer to the nearest cent gives us:
$359.25 ≈ $359.26
Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male is $359.26.
None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.
To know more about rounding., visit:
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Solve for x
X
18
24
16
Answers
Answer: should be 24?
Step-by-step explanation:
im not sure